Theorem pm5.44

Description: Theorem *5.44 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.44	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		jcab	⊢ ( ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ↔ ( ( 𝜑 → 𝜓 ) ∧ ( 𝜑 → 𝜒 ) ) )
2	1	baibr	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) )