Theorem ancomsd 269

Description: Deduction commuting conjunction in antecedent. (Contributed by NM, 12-Dec-2004.)

Hypothesis

Ref	Expression
ancomsd.1	⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))

Assertion

Ref	Expression
ancomsd	⊢ (𝜑 → ((𝜒 ∧ 𝜓) → 𝜃))

Proof of Theorem ancomsd

Step	Hyp	Ref	Expression
1		ancom 266	. 2 ⊢ ((𝜒 ∧ 𝜓) ↔ (𝜓 ∧ 𝜒))
2		ancomsd.1	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
3	1, 2	biimtrid 152	1 ⊢ (𝜑 → ((𝜒 ∧ 𝜓) → 𝜃))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  sylan2d  294  mpand  429  anabsi6  580  ralxfrd  4554  rexxfrd  4555  poirr2  5124  smoel  6457  genprndl  7724  genprndu  7725  addcanprlemu  7818  leltadd  8610  lemul12b  9024  lbzbi  9828  dvdssub2  12367  odzdvds  12789  wlk1walkdom  16131