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Theorem 3imp31 1276
Description: The importation inference 3imp 1275 with commutation of the first and third conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.)
Hypothesis
Ref Expression
3imp.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
3imp31 ((𝜒𝜓𝜑) → 𝜃)

Proof of Theorem 3imp31
StepHypRef Expression
1 3imp.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
21com13 88 . 2 (𝜒 → (𝜓 → (𝜑𝜃)))
323imp 1275 1 ((𝜒𝜓𝜑) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1054
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 197  df-an 385  df-3an 1056
This theorem is referenced by:  dvdsmodexp  15035  pthdadjvtx  26682  umgr2cwwk2dif  27028  clwlksf1clwwlklem  27055  frgrwopreglem2  27293
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