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Theorem com24 87
Description: Commutation of antecedents. Swap 2nd 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
com24 (𝜑 → (𝜃 → (𝜒 → (𝜓𝜏))))

Proof of Theorem com24
StepHypRef Expression
1 com4.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
21com4t 85 . 2 (𝜒 → (𝜃 → (𝜑 → (𝜓𝜏))))
32com13 80 1 (𝜑 → (𝜃 → (𝜒 → (𝜓𝜏))))
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:  com25  91  tfrlem9  6344  nnmordi  6541  fundmen  6832  fiintim  6957  elfzodifsumelfzo  10231  ssfzo12  10254  dvdsmodexp  11834  dvdsaddre2b  11880  infpnlem1  12391  grpinveu  12982  mulgass2  13410  lss1d  13699  cnpnei  14176
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