Theorem ancomsd

Description: Deduction commuting conjunction in antecedent. (Contributed by NM, 12-Dec-2004)

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

Proof

Step	Hyp	Ref	Expression
1		ancomsd.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
2	1	expcomd	⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) )
3	2	impd	⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜓 ) → 𝜃 ) )