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Theorem 3an1rs 1116
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 108 . . . . 5 ((𝜑𝜓𝜒) → (𝜃𝜏))
323exp 1103 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
43com34 77 . . 3 (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏))))
543imp 1098 . 2 ((𝜑𝜓𝜃) → (𝜒𝜏))
65imp 115 1 (((𝜑𝜓𝜃) ∧ 𝜒) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  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: (None)
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