Theorem bj-cbv3v2 32727

Description: Version of cbv3 2265 with two dv conditions, which does not require ax-11 2034 nor ax-13 2246. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bj-cbv3v2.nf	|- F/ x ps
bj-cbv3v2.1	|- ( x = y -> ( ph -> ps ) )

Assertion

Ref	Expression
bj-cbv3v2	|- ( A. x ph -> A. y ps )

Distinct variable groups:   x, y   ph, y

Allowed substitution hints:   ph( x)   ps( x, y)

Proof of Theorem bj-cbv3v2

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ y A. x ph
2		bj-cbv3v2.nf	. . 3 |- F/ x ps
3		bj-cbv3v2.1	. . 3 |- ( x = y -> ( ph -> ps ) )
4	2, 3	spimv1 2115	. 2 |- ( A. x ph -> ps )
5	1, 4	alrimi 2082	1 |- ( A. x ph -> A. y ps )

Syntax hints:   -> wi 4   A.wal 1481   F/wnf 1708

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-ex 1705  df-nf 1710

This theorem is referenced by:  bj-cbv3hv2  32728