Theorem ancoms

Description: Inference commuting conjunction in antecedent. (Contributed by NM, 21-Apr-1994)

	Ref	Expression
Hypothesis	ancoms.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	ancoms	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		ancoms.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2	1	expcom	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
3	2	imp	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 )