Theorem equs5aALT

Description: Alternate proof of equs5a . Uses ax-12 but not ax-13 . (Contributed by NM, 2-Feb-2007) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	equs5aALT	|- ( E. x ( x = y /\ A. y ph ) -> A. x ( x = y -> ph ) )

Proof

Step	Hyp	Ref	Expression
1		nfa1	|- F/ x A. x ( x = y -> ph )
2		ax-12	|- ( x = y -> ( A. y ph -> A. x ( x = y -> ph ) ) )
3	2	imp	|- ( ( x = y /\ A. y ph ) -> A. x ( x = y -> ph ) )
4	1 3	exlimi	|- ( E. x ( x = y /\ A. y ph ) -> A. x ( x = y -> ph ) )