Theorem an31s 667

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 425	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	com13 89	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
4	3	imp31 423	1 ⊢ (((𝜒 ∧ 𝜓) ∧ 𝜑) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  icoopnst  25260  bddiblnc  26162  grpoidinvlem3  31108  kbop  32555