Theorem pm5.42

Description: Theorem *5.42 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.42	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) ↔ ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜒 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		ibar	⊢ ( 𝜑 → ( 𝜒 ↔ ( 𝜑 ∧ 𝜒 ) ) )
2	1	imbi2d	⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → ( 𝜑 ∧ 𝜒 ) ) ) )
3	2	pm5.74i	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) ↔ ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜒 ) ) ) )