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Theorem an31s 843
Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.)
Hypothesis
Ref Expression
an32s.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
an31s (((𝜒𝜓) ∧ 𝜑) → 𝜃)

Proof of Theorem an31s
StepHypRef Expression
1 an32s.1 . . . 4 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
21exp31 627 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
32com13 85 . 2 (𝜒 → (𝜓 → (𝜑𝜃)))
43imp31 446 1 (((𝜒𝜓) ∧ 𝜑) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-an 384
This theorem is referenced by:  icoopnst  22477  grpoidinvlem3  26510  kbop  28002  frmin  30789  bddiblnc  32446
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