ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  an13s GIF version

Theorem an13s 541
Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.)
Hypothesis
Ref Expression
an12s.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
an13s ((𝜒 ∧ (𝜓𝜑)) → 𝜃)

Proof of Theorem an13s
StepHypRef Expression
1 an12s.1 . . . 4 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
21exp32 362 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
32com13 80 . 2 (𝜒 → (𝜓 → (𝜑𝜃)))
43imp32 255 1 ((𝜒 ∧ (𝜓𝜑)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator