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Theorem ancomsd 260
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 257 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
2 ancomsd.1 . 2 (𝜑 → ((𝜓𝜒) → 𝜃))
31, 2syl5bi 145 1 (𝜑 → ((𝜒𝜓) → 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 depends on definitions:  df-bi 114
This theorem is referenced by:  sylan2d  282  mpand  413  anabsi6  522  ralxfrd  4221  rexxfrd  4222  poirr2  4744  smoel  5945  genprndl  6676  genprndu  6677  addcanprlemu  6770  leltadd  7515  lemul12b  7901  lbzbi  8647  dvdssub2  10148
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