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Theorem ancomsd 267
 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 264 . 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  290  mpand  423  anabsi6  550  ralxfrd  4321  rexxfrd  4322  poirr2  4867  smoel  6127  genprndl  7230  genprndu  7231  addcanprlemu  7324  leltadd  8076  lemul12b  8477  lbzbi  9258  dvdssub2  11330
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