Theorem ch2varv 15874

Description: Version of ch2var 15873 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 1552	. 2 |- F/ x ps
2		nfv 1552	. 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 15873	1 |- ps

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485

This theorem is referenced by:  sscoll2  16093