Theorem pm5.41

Description: Theorem *5.41 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 12-Oct-2012)

	Ref	Expression
Assertion	pm5.41	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) ↔ ( 𝜑 → ( 𝜓 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imdi	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) ↔ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) )
2	1	bicomi	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) ↔ ( 𝜑 → ( 𝜓 → 𝜒 ) ) )