ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3an1rs GIF version

Theorem 3an1rs 1153
Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007.)
Hypothesis
Ref Expression
3an1rs.1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
3an1rs (((𝜑𝜓𝜃) ∧ 𝜒) → 𝜏)

Proof of Theorem 3an1rs
StepHypRef Expression
1 3an1rs.1 . . . . . 6 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
21ex 113 . . . . 5 ((𝜑𝜓𝜒) → (𝜃𝜏))
323exp 1140 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
43com34 82 . . 3 (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏))))
543imp 1135 . 2 ((𝜑𝜓𝜃) → (𝜒𝜏))
65imp 122 1 (((𝜑𝜓𝜃) ∧ 𝜒) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 924
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator