Theorem bj-vexwv 32857

Description: Version of bj-vexw 32855 with a dv condition, which does not require ax-13 2246. The degenerate instance of bj-vexw 32855 is a simple consequence of abid 2610 (which does not depend on ax-13 2246 either). (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-vexwv.1	|- ph

Assertion

Ref	Expression
bj-vexwv	|- y e. { x | ph }

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem bj-vexwv

Step	Hyp	Ref	Expression
1		bj-vexwvt 32856	. 2 |- ( A. x ph -> y e. { x | ph } )
2		bj-vexwv.1	. 2 |- ph
3	1, 2	mpg 1724	1 |- y e. { x | ph }

Syntax hints:   e. wcel 1990   {cab 2608

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-an 386  df-ex 1705  df-sb 1881  df-clab 2609

This theorem is referenced by:  bj-denotes  32858  bj-rexvwv  32866  bj-rababwv  32867  bj-df-v  33016