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Theorem 3imp31 1249
Description: The importation inference 3imp 1248 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 85 . 2 (𝜒 → (𝜓 → (𝜑𝜃)))
323imp 1248 1 ((𝜒𝜓𝜑) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1030
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  df-3an 1032
This theorem is referenced by:  pthdadjvtx  40917  umgr2cwwk2dif  41229  clwlksf1clwwlklem  41256  frgrwopreglem2  41463  av-numclwwlkffin0  41494
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