Theorem ancomsd 440

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 437	. 2 ⊢ ((χ ∧ ψ) ↔ (ψ ∧ χ))
2		ancomsd.1	. 2 ⊢ (φ → ((ψ ∧ χ) → θ))
3	1, 2	syl5bi 208	1 ⊢ (φ → ((χ ∧ ψ) → θ))

Syntax hints:   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  sylan2d  468  mpand  656  anabsi6  791  ralcom2  2776  enprmaplem3  6079