Theorem imdistanri

Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002)

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

Proof

Step	Hyp	Ref	Expression
1		imdistanri.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	com12	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
3	2	impac	⊢ ( ( 𝜓 ∧ 𝜑 ) → ( 𝜒 ∧ 𝜑 ) )