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Theorem 3imp21 1105
 Description: The importation inference 3imp 1101 with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.) (Revised to shorten 3com12 1117 by Wolf Lammen, 23-Jun-2022.)
Hypothesis
Ref Expression
3imp.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
3imp21 ((𝜓𝜑𝜒) → 𝜃)

Proof of Theorem 3imp21
StepHypRef Expression
1 3imp.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
21com13 88 . 2 (𝜒 → (𝜓 → (𝜑𝜃)))
323imp231 1104 1 ((𝜓𝜑𝜒) → 𝜃)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1072 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 1074 This theorem is referenced by:  3com12  1117  sotri3  5676  elfz1b  12594  gausslemma2dlem1a  25281  upgrewlkle2  26704  pthdivtx  26827  clwwlkinwwlk  27161  clwlksfclwwlkOLD  27208  upgr3v3e3cycl  27324  upgr4cycl4dv4e  27329  numclwwlk2lem1lem  27490  frgrregord013  27555  ax6e2ndeqALT  39658  fmtnofac2  41983
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