Theorem pm3.43

Description: Theorem *3.43 (Comp) of WhiteheadRussell p. 113. (Contributed by NM, 3-Jan-2005)

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

Proof

Step	Hyp	Ref	Expression
1		pm3.43i	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) )
2	1	imp	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜑 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) )