Theorem bj-spimevv 32722

Description: Version of spimev 2259 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-spimevv.1	|- ( x = y -> ( ph -> ps ) )

Assertion

Ref	Expression
bj-spimevv	|- ( ph -> E. x ps )

Distinct variable groups:   x, y   ph, x

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

Proof of Theorem bj-spimevv

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ x ph
2		bj-spimevv.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	bj-spimev 32720	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1704

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  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by:  bj-axsep  32793  bj-dtru  32797