[Discrete Math]proof of unique existence statement by the rules of inference for propositional and predicate logic

[alllovemewai]

Recall that we can express unique existence as

(1) ∃x(P (x) ∧ ∀y(P (y) → x = y))

In many unique existence proofs, instead of proving (1), we prove the following:

(2) ∃xP (x)
(3) ∀x∀y(P (x) ∧ P (y) → x = y)

Your task here is to prove (1) from (2) and (3) using the rules of inference
for propositional and predicate logic.

I have tried it by different law but I am not sure the answer, I appreciate for someone help.

 

[Deleted member 4993]

Recall that we can express unique existence as

(1) ∃x(P (x) ∧ ∀y(P (y) → x = y))

In many unique existence proofs, instead of proving (1), we prove the following:

(2) ∃xP (x)
(3) ∀x∀y(P (x) ∧ P (y) → x = y)

Your task here is to prove (1) from (2) and (3) using the rules of inference
for propositional and predicate logic.

I have tried it by different law but I am not sure the answer, I appreciate for someone help.

Please show us what you have tried and exactly where you are stuck.

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[jakeperalta]

LOL I guess we are studying the same course. Here is what I've done so far. I believe I got it wrong at step 4 but I have no idea how to do this kind of question.