Theorem an13s 557

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 363	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	com13 80	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
4	3	imp32 255	1 ⊢ ((𝜒 ∧ (𝜓 ∧ 𝜑)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 103

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

This theorem is referenced by: (None)