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Theorem 3com13 1146
Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3com13 ((𝜒𝜓𝜑) → 𝜃)

Proof of Theorem 3com13
StepHypRef Expression
1 3anrev 932 . 2 ((𝜒𝜓𝜑) ↔ (𝜑𝜓𝜒))
2 3exp.1 . 2 ((𝜑𝜓𝜒) → 𝜃)
31, 2sylbi 119 1 ((𝜒𝜓𝜑) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 924
This theorem is referenced by:  3coml  1148  3adant3l  1168  3adant3r  1169  syld3an1  1218  oaword1  6186  nnacan  6223  elmapg  6370  subadd  7629  xrltso  9198  iooshf  9302  dvdsmulc  10706  lcmdvdsb  10948
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