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Theorem ancom1s 511
Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)
Hypothesis
Ref Expression
an32s.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
ancom1s (((𝜓𝜑) ∧ 𝜒) → 𝜃)

Proof of Theorem ancom1s
StepHypRef Expression
1 pm3.22 256 . 2 ((𝜓𝜑) → (𝜑𝜓))
2 an32s.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 271 1 (((𝜓𝜑) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
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 is referenced by:  bilukdc  1303  prarloc  6658  leltadd  7515  divmul13ap  7765  modqmulmodr  9339  fzomaxdif  9939
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