Theorem bj-2stdpc4v 32755

Description: Version of 2stdpc4 2354 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-2stdpc4v	|- ( A. x A. y ph -> [ z / x ] [ w / y ] ph )

Distinct variable groups:   x, z   y, w

Allowed substitution hints:   ph( x, y, z, w)

Proof of Theorem bj-2stdpc4v

Step	Hyp	Ref	Expression
1		bj-stdpc4v 32754	. . 3 |- ( A. y ph -> [ w / y ] ph )
2	1	alimi 1739	. 2 |- ( A. x A. y ph -> A. x [ w / y ] ph )
3		bj-stdpc4v 32754	. 2 |- ( A. x [ w / y ] ph -> [ z / x ] [ w / y ] ph )
4	2, 3	syl 17	1 |- ( A. x A. y ph -> [ z / x ] [ w / y ] 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: (None)