Theorem imdistani

Description: Distribution of implication with conjunction. (Contributed by NM, 1-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		imdistani.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	anc2li	⊢ ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜒 ) ) )
3	2	imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ∧ 𝜒 ) )