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  582  ralxfrd  4582  rexxfrd  4583  poirr2  5154  smoel  6530  genprndl  7832  genprndu  7833  addcanprlemu  7926  leltadd  8717  lemul12b  9131  lbzbi  9944  dvdssub2  12514  odzdvds  12936  wlk1walkdom  16341