Theorem equsexvwOLD

Description: Obsolete version of equsexvw as of 23-Oct-2023. (Contributed by BJ, 31-May-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	equsalvw.1	|- ( x = y -> ( ph <-> ps ) )
Assertion	equsexvwOLD	|- ( E. x ( x = y /\ ph ) <-> ps )

Proof

Step	Hyp	Ref	Expression
1		equsalvw.1	|- ( x = y -> ( ph <-> ps ) )
2	1	pm5.32i	|- ( ( x = y /\ ph ) <-> ( x = y /\ ps ) )
3	2	exbii	|- ( E. x ( x = y /\ ph ) <-> E. x ( x = y /\ ps ) )
4		ax6ev	|- E. x x = y
5		19.41v	|- ( E. x ( x = y /\ ps ) <-> ( E. x x = y /\ ps ) )
6	4 5	mpbiran	|- ( E. x ( x = y /\ ps ) <-> ps )
7	3 6	bitri	|- ( E. x ( x = y /\ ph ) <-> ps )