Theorem bj-equsvt

Description: A variant of equsv . (Contributed by BJ, 7-Oct-2024)

	Ref	Expression
Assertion	bj-equsvt	|- ( F// x ph -> ( A. x ( x = y -> ph ) <-> ph ) )

Proof

Step	Hyp	Ref	Expression
1		bj-19.23t	|- ( F// x ph -> ( A. x ( x = y -> ph ) <-> ( E. x x = y -> ph ) ) )
2		ax6ev	|- E. x x = y
3	2	a1bi	|- ( ph <-> ( E. x x = y -> ph ) )
4	1 3	bitr4di	|- ( F// x ph -> ( A. x ( x = y -> ph ) <-> ph ) )