Theorem ancom1s 780

Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)

Hypothesis

Ref	Expression
an32s.1	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Assertion

Ref	Expression
ancom1s	⊢ (((ψ ∧ φ) ∧ χ) → θ)

Proof of Theorem ancom1s

Step	Hyp	Ref	Expression
1		pm3.22 436	. 2 ⊢ ((ψ ∧ φ) → (φ ∧ ψ))
2		an32s.1	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
3	1, 2	sylan 457	1 ⊢ (((ψ ∧ φ) ∧ χ) → 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: (None)