ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  com24 GIF version

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  6295  nnmordi  6492  fundmen  6780  fiintim  6902  elfzodifsumelfzo  10144  ssfzo12  10167  dvdsmodexp  11744  infpnlem1  12298  grpinveu  12728  cnpnei  12972
  Copyright terms: Public domain W3C validator