Theorem an12s 776

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 772 is combined with syl 15 (or a variant). (Contributed by NM, 13-Mar-1996.)

Hypothesis

Ref	Expression
an12s.1	⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Assertion

Ref	Expression
an12s	⊢ ((ψ ∧ (φ ∧ χ)) → θ)

Proof of Theorem an12s

Step	Hyp	Ref	Expression
1		an12 772	. 2 ⊢ ((ψ ∧ (φ ∧ χ)) ↔ (φ ∧ (ψ ∧ χ)))
2		an12s.1	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	1, 2	sylbi 187	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:  anabsan2  795