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Theorem 3imp31 1109
 Description: The importation inference 3imp 1108 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 1108 1 ((𝜒𝜓𝜑) → 𝜃)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1084 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 210  df-an 400  df-3an 1086 This theorem is referenced by:  3com13  1121  dvdsmodexp  15611  gsummatr01lem4  21267  elntg2  26783  pthdadjvtx  27523  umgr2cwwk2dif  27853  frgrwopreglem2  28102  relexpxpmin  40411  prproropf1olem4  44016  resum2sqorgt0  45116
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