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Theorem ch2varv 12902
Description: Version of ch2var 12901 with non-freeness 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
StepHypRef Expression
1 nfv 1493 . 2  |-  F/ x ps
2 nfv 1493 . 2  |-  F/ z ps
3 ch2varv.maj . 2  |-  ( ( x  =  y  /\  z  =  t )  ->  ( ph  <->  ps )
)
4 ch2varv.min . 2  |-  ph
51, 2, 3, 4ch2var 12901 1  |-  ps
Colors of variables: wff set class
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  sscoll2  13113
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