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

Theorem chvarv 1907
Description: Implicit substitution of 𝑦 for 𝑥 into a theorem. (Contributed by NM, 20-Apr-1994.)
Hypotheses
Ref Expression
chv.1 (𝑥 = 𝑦 → (𝜑𝜓))
chv.2 𝜑
Assertion
Ref Expression
chvarv 𝜓
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem chvarv
StepHypRef Expression
1 chv.1 . . 3 (𝑥 = 𝑦 → (𝜑𝜓))
21spv 1832 . 2 (∀𝑥𝜑𝜓)
3 chv.2 . 2 𝜑
42, 3mpg 1427 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 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:  axext3  2120  axsep2  4042  tz6.12f  5443  ltordlem  8237  bdsep2  13069  strcoll2  13166
  Copyright terms: Public domain W3C validator