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Theorem com13 74
Description: Commutation of antecedents. Swap 1st and 3rd. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)
Hypothesis
Ref Expression
com3.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
com13 (𝜒 → (𝜓 → (𝜑𝜃)))

Proof of Theorem com13
StepHypRef Expression
1 com3.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
21com3r 73 . 2 (𝜒 → (𝜑 → (𝜓𝜃)))
32com23 72 1 (𝜒 → (𝜓 → (𝜑𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  com24  81  an13s  501  an31s  504  funopg  4934  f1o2ndf1  5849  brecop  6196  elfz0ubfz0  8980  elfz0fzfz0  8981  fz0fzelfz0  8982  fz0fzdiffz0  8985  fzo1fzo0n0  9037  elfzodifsumelfzo  9055  ssfzo12  9078  ssfzo12bi  9079  sqrt2irr  9852  bj-inf2vnlem2  10070
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