Theorem an31s 570

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

Hypothesis

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

Assertion

Ref	Expression
an31s	⊢ (((𝜒 ∧ 𝜓) ∧ 𝜑) → 𝜃)

Proof of Theorem an31s

Step	Hyp	Ref	Expression
1		an32s.1	. . . 4 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
2	1	exp31 364	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	com13 80	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
4	3	imp31 256	1 ⊢ (((𝜒 ∧ 𝜓) ∧ 𝜑) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  genpassl  7591  genpassu  7592