Theorem bj-vexwvt 32856

Description: Closed form of bj-vexwv 32857 and version of bj-vexwt 32854 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-vexwvt	|- ( A. x ph -> y e. { x | ph } )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem bj-vexwvt

Step	Hyp	Ref	Expression
1		bj-stdpc4v 32754	. 2 |- ( A. x ph -> [ y / x ] ph )
2		df-clab 2609	. 2 |- ( y e. { x | ph } <-> [ y / x ] ph )
3	1, 2	sylibr 224	1 |- ( A. x ph -> y e. { x | ph } )

Syntax hints:   -> wi 4   A.wal 1481   [wsb 1880   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-vexwv  32857  bj-issetwt  32859  bj-abv  32901