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Theorem ch2varv 11012
Description: Version of ch2var 11011 with non-freeness hypotheses replaced by DV 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 1462 . 2 𝑥𝜓
2 nfv 1462 . 2 𝑧𝜓
3 ch2varv.maj . 2 ((𝑥 = 𝑦𝑧 = 𝑡) → (𝜑𝜓))
4 ch2varv.min . 2 𝜑
51, 2, 3, 4ch2var 11011 1 𝜓
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  sscoll2  11226
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