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Theorem com14 88
Description: Commutation of antecedents. Swap 1st and 4th. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)
Hypothesis
Ref Expression
com4.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
com14 (𝜃 → (𝜓 → (𝜒 → (𝜑𝜏))))

Proof of Theorem com14
StepHypRef Expression
1 com4.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
21com4l 84 . 2 (𝜓 → (𝜒 → (𝜃 → (𝜑𝜏))))
32com3r 79 1 (𝜃 → (𝜓 → (𝜒 → (𝜑𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  f1o2ndf1  6125  fiintim  6817  fz0fzdiffz0  9919  elfzodifsumelfzo  9990  ssfzo12  10013  dfgcd2  11713  cncongr1  11795
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