Theorem bj-stdpc4v 32754

Description: Version of stdpc4 2353 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-stdpc4v	|- ( A. x ph -> [ y / x ] ph )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem bj-stdpc4v

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 |- ( ph -> ( x = y -> ph ) )
2	1	alimi 1739	. 2 |- ( A. x ph -> A. x ( x = y -> ph ) )
3		bj-sb2v 32753	. 2 |- ( A. x ( x = y -> ph ) -> [ y / x ] ph )
4	2, 3	syl 17	1 |- ( A. x ph -> [ y / x ] ph )

Syntax hints:   -> wi 4   A.wal 1481   [wsb 1880

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

This theorem is referenced by:  bj-2stdpc4v  32755  bj-sbftv  32763  bj-sbfvv  32765  bj-sbtv  32766  bj-vexwvt  32856  bj-ab0  32902