ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3comr GIF version

Theorem 3comr 1112
Description: Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3comr ((𝜒𝜑𝜓) → 𝜃)

Proof of Theorem 3comr
StepHypRef Expression
1 3exp.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213coml 1111 . 2 ((𝜓𝜒𝜑) → 𝜃)
323coml 1111 1 ((𝜒𝜑𝜓) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  nnacan  6085  le2tri3i  7126  ltaddsublt  7562  div12ap  7673  lemul12b  7827  zdivadd  8329  zdivmul  8330  elfz  8880  fzmmmeqm  8921  fzrev  8946  absdiflt  9688  absdifle  9689
  Copyright terms: Public domain W3C validator