Theorem pm3.31

Description: Theorem *3.31 (Imp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 24-Mar-2013)

	Ref	Expression
Assertion	pm3.31	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )
2	1	impd	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )