Theorem ancomsd 267

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 264	. 2 ⊢ ((𝜒 ∧ 𝜓) ↔ (𝜓 ∧ 𝜒))
2		ancomsd.1	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
3	1, 2	syl5bi 151	1 ⊢ (𝜑 → ((𝜒 ∧ 𝜓) → 𝜃))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  sylan2d  290  mpand  423  anabsi6  550  ralxfrd  4321  rexxfrd  4322  poirr2  4867  smoel  6127  genprndl  7230  genprndu  7231  addcanprlemu  7324  leltadd  8076  lemul12b  8477  lbzbi  9258  dvdssub2  11330