Theorem equsexvOLD

Description: Obsolete version of equsexv as of 18-Nov-2024. (Contributed by NM, 5-Aug-1993) (Revised by BJ, 31-May-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	equsalv.nf	|- F/ x ps
	equsalv.1	|- ( x = y -> ( ph <-> ps ) )
Assertion	equsexvOLD	|- ( E. x ( x = y /\ ph ) <-> ps )

Proof

Step	Hyp	Ref	Expression
1		equsalv.nf	|- F/ x ps
2		equsalv.1	|- ( x = y -> ( ph <-> ps ) )
3		sbalex	|- ( E. x ( x = y /\ ph ) <-> A. x ( x = y -> ph ) )
4	1 2	equsalv	|- ( A. x ( x = y -> ph ) <-> ps )
5	3 4	bitri	|- ( E. x ( x = y /\ ph ) <-> ps )