Theorem pm3.43i

Description: Nested conjunction of antecedents. (Contributed by NM, 4-Jan-1993)

	Ref	Expression
Assertion	pm3.43i	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.2	⊢ ( 𝜓 → ( 𝜒 → ( 𝜓 ∧ 𝜒 ) ) )
2	1	imim3i	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) )