ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  chvarvv GIF version

Theorem chvarvv 1901
Description: Version of chvarv 1930 with a disjoint variable condition. (Contributed by BJ, 31-May-2019.)
Hypotheses
Ref Expression
chvarvv.1 (𝑥 = 𝑦 → (𝜑𝜓))
chvarvv.2 𝜑
Assertion
Ref Expression
chvarvv 𝜓
Distinct variable groups:   𝑥,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem chvarvv
StepHypRef Expression
1 chvarvv.1 . . 3 (𝑥 = 𝑦 → (𝜑𝜓))
21spvv 1900 . 2 (∀𝑥𝜑𝜓)
3 chvarvv.2 . 2 𝜑
42, 3mpg 1444 1 𝜓
Colors of variables: wff set class
Syntax hints:  wi 4  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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-nf 1454
This theorem is referenced by:  prodfdivap  11497
  Copyright terms: Public domain W3C validator