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Theorem an12s 565
Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 561 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 561 . 2 ((𝜓 ∧ (𝜑𝜒)) ↔ (𝜑 ∧ (𝜓𝜒)))
2 an12s.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylbi 121 1 ((𝜓 ∧ (𝜑𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  anabsan2  584  1stconst  6219  2ndconst  6220  sbthlemi5  6957  iccshftr  9990  iccshftl  9992  iccdil  9994  icccntr  9996  zfz1iso  10814  ndvdsadd  11928  neipsm  13525
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