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Theorem 3imp21 1268
Description: The importation inference 3imp 1248 with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.)
Hypothesis
Ref Expression
3imp21.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
3imp21 ((𝜓𝜑𝜒) → 𝜃)

Proof of Theorem 3imp21
StepHypRef Expression
1 3imp21.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
213imp 1248 . 2 ((𝜑𝜓𝜒) → 𝜃)
323com12 1260 1 ((𝜓𝜑𝜒) → 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:  sotri3  5431  gausslemma2dlem1a  24834  ax6e2ndeqALT  37972  fmtnofac2  39803  upgrewlkle2  40789  pthdivtx  40916  clwlksfclwwlk  41250  upgr3v3e3cycl  41328  upgr4cycl4dv4e  41333  av-extwwlkfablem2  41491  av-numclwwlkovf2ex  41498  av-frgraregord013  41530
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