Theorem imdistand

Description: Distribution of implication with conjunction (deduction form). (Contributed by NM, 27-Aug-2004)

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

Proof

Step	Hyp	Ref	Expression
1		imdistand.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		imdistan	⊢ ( ( 𝜓 → ( 𝜒 → 𝜃 ) ) ↔ ( ( 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) ) )
3	1 2	sylib	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) ) )