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  4498  rexxfrd  4499  poirr2  5063  smoel  6367  genprndl  7607  genprndu  7608  addcanprlemu  7701  leltadd  8493  lemul12b  8907  lbzbi  9709  dvdssub2  12019  odzdvds  12441