Theorem an13s

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

	Ref	Expression
Hypothesis	an12s.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion	an13s	⊢ ( ( 𝜒 ∧ ( 𝜓 ∧ 𝜑 ) ) → 𝜃 )

Proof

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