Theorem wl-cbv3vv 33307

Description: Avoiding ax-11 2034. (Contributed by Wolf Lammen, 30-Aug-2021.)

Hypotheses

Ref	Expression
wl-cbv3vv.nf	|- F/ x ps
wl-cbv3vv.1	|- ( x = y -> ( ph -> ps ) )

Assertion

Ref	Expression
wl-cbv3vv	|- ( A. x ph -> A. y ps )

Distinct variable groups:   x, y   ph, y

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

Proof of Theorem wl-cbv3vv

Step	Hyp	Ref	Expression
1		wl-cbv3vv.nf	. . 3 |- F/ x ps
2		wl-cbv3vv.1	. . 3 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spimv1 2115	. 2 |- ( A. x ph -> ps )
4	3	alrimiv 1855	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: (None)