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Theorem ch2varv 13005
Description: Version of ch2var 13004 with non-freeness hypotheses replaced with disjoint variable conditions. (Contributed by BJ, 17-Oct-2019.)
Hypotheses
Ref Expression
ch2varv.maj ((𝑥 = 𝑦𝑧 = 𝑡) → (𝜑𝜓))
ch2varv.min 𝜑
Assertion
Ref Expression
ch2varv 𝜓
Distinct variable groups:   𝑥,𝑧,𝜓   𝑥,𝑡
Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧,𝑡)   𝜓(𝑦,𝑡)

Proof of Theorem ch2varv
StepHypRef Expression
1 nfv 1508 . 2 𝑥𝜓
2 nfv 1508 . 2 𝑧𝜓
3 ch2varv.maj . 2 ((𝑥 = 𝑦𝑧 = 𝑡) → (𝜑𝜓))
4 ch2varv.min . 2 𝜑
51, 2, 3, 4ch2var 13004 1 𝜓
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  sscoll2  13216
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