Theorem bj-chvarvv 32726

Description: Version of chvarv 2263 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bj-chvarvv.1	|- ( x = y -> ( ph <-> ps ) )
bj-chvarvv.2	|- ph

Assertion

Ref	Expression
bj-chvarvv	|- ps

Distinct variable groups:   x, y   ps, x

Allowed substitution hints:   ph( x, y)   ps( y)

Proof of Theorem bj-chvarvv

Step	Hyp	Ref	Expression
1		bj-chvarvv.1	. . 3 |- ( x = y -> ( ph <-> ps ) )
2	1	bj-spvv 32723	. 2 |- ( A. x ph -> ps )
3		bj-chvarvv.2	. 2 |- ph
4	2, 3	mpg 1724	1 |- ps

Syntax hints:   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  bj-axext3  32769  bj-axrep1  32788  bj-axsep2  32921