Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  ch2varv GIF version

Theorem ch2varv 11313
Description: Version of ch2var 11312 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 1466 . 2 𝑥𝜓
2 nfv 1466 . 2 𝑧𝜓
3 ch2varv.maj . 2 ((𝑥 = 𝑦𝑧 = 𝑡) → (𝜑𝜓))
4 ch2varv.min . 2 𝜑
51, 2, 3, 4ch2var 11312 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 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  sscoll2  11527
  Copyright terms: Public domain W3C validator