Theorem an13s 778

Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.)

Hypothesis

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

Assertion

Ref	Expression
an13s	⊢ ((χ ∧ (ψ ∧ φ)) → θ)

Proof of Theorem an13s

Step	Hyp	Ref	Expression
1		an12s.1	. . . 4 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
2	1	exp32 588	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	com13 74	. 2 ⊢ (χ → (ψ → (φ → θ)))
4	3	imp32 422	1 ⊢ ((χ ∧ (ψ ∧ φ)) → 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)