Theorem bj-vexwt 32854

Description: Closed form of bj-vexw 32855. (Contributed by BJ, 14-Jun-2019.) (Proof modification is discouraged.) Use bj-vexwvt 32856 instead when sufficient. (New usage is discouraged.)

Assertion

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

Proof of Theorem bj-vexwt

Step	Hyp	Ref	Expression
1		stdpc4 2353	. 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  ax-13 2246

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-vexw  32855