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Theorem 3com13 1120
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 906 . 2 ((𝜒𝜓𝜑) ↔ (𝜑𝜓𝜒))
2 3exp.1 . 2 ((𝜑𝜓𝜒) → 𝜃)
31, 2sylbi 118 1 ((𝜒𝜓𝜑) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  3coml  1122  3adant3l  1142  3adant3r  1143  syld3an1  1192  oaword1  6081  nnacan  6116  subadd  7277  xrltso  8818  iooshf  8922  elfzmlbmOLD  9091  dvdsmulc  10135
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