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Theorem an12s 532
Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 528 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 528 . 2 ((𝜓 ∧ (𝜑𝜒)) ↔ (𝜑 ∧ (𝜓𝜒)))
2 an12s.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylbi 119 1 ((𝜓 ∧ (𝜑𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
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
This theorem is referenced by:  anabsan2  551  1stconst  5986  2ndconst  5987  sbthlemi5  6670  iccshftr  9411  iccshftl  9413  iccdil  9415  icccntr  9417  zfz1iso  10246  ndvdsadd  11209
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