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  433  anabsi6  586  ralxfrd  4606  rexxfrd  4607  poirr2  5178  smoel  6565  genprndl  7882  genprndu  7883  addcanprlemu  7976  leltadd  8769  lemul12b  9185  lbzbi  9999  dvdssub2  12585  odzdvds  13007  wlk1walkdom  16583