Theorem ch2varv 13649

Description: Version of ch2var 13648 with nonfreeness hypotheses replaced with disjoint variable conditions. (Contributed by BJ, 17-Oct-2019.)

Hypotheses

Ref	Expression
ch2varv.maj	|- ( ( x = y /\ z = t ) -> ( ph <-> ps ) )
ch2varv.min	|- ph

Assertion

Ref	Expression
ch2varv	|- ps

Distinct variable groups:   x, z, ps   x, t

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

Proof of Theorem ch2varv

Step	Hyp	Ref	Expression
1		nfv 1516	. 2 |- F/ x ps
2		nfv 1516	. 2 |- F/ z ps
3		ch2varv.maj	. 2 |- ( ( x = y /\ z = t ) -> ( ph <-> ps ) )
4		ch2varv.min	. 2 |- ph
5	1, 2, 3, 4	ch2var 13648	1 |- ps

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-nf 1449

This theorem is referenced by:  sscoll2  13870