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Theorem an12s 537
Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 533 is combined with syl 14 (or a variant). (Contributed by NM, 13-Mar-1996.)
Hypothesis
Ref Expression
an12s.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
an12s ((𝜓 ∧ (𝜑𝜒)) → 𝜃)

Proof of Theorem an12s
StepHypRef Expression
1 an12 533 . 2 ((𝜓 ∧ (𝜑𝜒)) ↔ (𝜑 ∧ (𝜓𝜒)))
2 an12s.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylbi 120 1 ((𝜓 ∧ (𝜑𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anabsan2  556  1stconst  6084  2ndconst  6085  sbthlemi5  6815  iccshftr  9717  iccshftl  9719  iccdil  9721  icccntr  9723  zfz1iso  10524  ndvdsadd  11524  neipsm  12218
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