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Theorem ancomsd 266
Description: Deduction commuting conjunction in antecedent. (Contributed by NM, 12-Dec-2004.)
Hypothesis
Ref Expression
ancomsd.1 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
ancomsd (𝜑 → ((𝜒𝜓) → 𝜃))

Proof of Theorem ancomsd
StepHypRef Expression
1 ancom 263 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
2 ancomsd.1 . 2 (𝜑 → ((𝜓𝜒) → 𝜃))
31, 2syl5bi 151 1 (𝜑 → ((𝜒𝜓) → 𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  sylan2d  289  mpand  421  anabsi6  548  ralxfrd  4297  rexxfrd  4298  poirr2  4837  smoel  6079  genprndl  7141  genprndu  7142  addcanprlemu  7235  leltadd  7986  lemul12b  8383  lbzbi  9162  dvdssub2  11177
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