If we have ∃x[P(x) & x=y], can we conclude P(y)?
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If you can do it, what would be the rule you're invoking? If it can be done, is it like existential instantiation on a term that isn't new since you know x=y?
logic
asked Nov 20 at 3:00
M. Moe
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If you can do it, what would be the rule you're invoking? If it can be done, is it like existential instantiation on a term that isn't new since you know x=y?
logic
asked Nov 20 at 3:00
M. Moe
31
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If you can do it, what would be the rule you're invoking? If it can be done, is it like existential instantiation on a term that isn't new since you know x=y?
logic
asked Nov 20 at 3:00
M. Moe
31
If you can do it, what would be the rule you're invoking? If it can be done, is it like existential instantiation on a term that isn't new since you know x=y?
logic
logic
asked Nov 20 at 3:00
M. Moe
31
asked Nov 20 at 3:00
M. Moe
31
asked Nov 20 at 3:00
M. Moe
31
asked Nov 20 at 3:00
M. Moe
31
asked Nov 20 at 3:00
M. Moe
31
31
add a comment |
add a comment |
1 Answer
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Sure you can infer it:
Let $a$ be the witness for the existential:
$P(a) land a=y$
Then use $land$ Elimination twice:
$P(a)$
$a=y$
Finally use $=$ Elimination on these two statements:
$P(y)$
answered Nov 20 at 3:22
Bram28
58.7k44185
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Sure you can infer it:
Let $a$ be the witness for the existential:
$P(a) land a=y$
Then use $land$ Elimination twice:
$P(a)$
$a=y$
Finally use $=$ Elimination on these two statements:
$P(y)$
answered Nov 20 at 3:22
Bram28
58.7k44185
add a comment |
up vote
1
down vote
accepted
Sure you can infer it:
Let $a$ be the witness for the existential:
$P(a) land a=y$
Then use $land$ Elimination twice:
$P(a)$
$a=y$
Finally use $=$ Elimination on these two statements:
$P(y)$
answered Nov 20 at 3:22
Bram28
58.7k44185
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Sure you can infer it:
Let $a$ be the witness for the existential:
$P(a) land a=y$
Then use $land$ Elimination twice:
$P(a)$
$a=y$
Finally use $=$ Elimination on these two statements:
$P(y)$
answered Nov 20 at 3:22
Bram28
58.7k44185
Sure you can infer it:
Let $a$ be the witness for the existential:
$P(a) land a=y$
Then use $land$ Elimination twice:
$P(a)$
$a=y$
Finally use $=$ Elimination on these two statements:
$P(y)$
answered Nov 20 at 3:22
Bram28
58.7k44185
answered Nov 20 at 3:22
Bram28
58.7k44185
answered Nov 20 at 3:22
Bram28
58.7k44185
answered Nov 20 at 3:22
Bram28
58.7k44185
58.7k44185
add a comment |
add a comment |
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