Theorem pm3.37

Description: Theorem *3.37 (Transp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 23-Oct-2012)

	Ref	Expression
Assertion	pm3.37	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) → ( ( 𝜑 ∧ ¬ 𝜒 ) → ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm4.14	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ∧ ¬ 𝜒 ) → ¬ 𝜓 ) )
2	1	biimpi	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) → ( ( 𝜑 ∧ ¬ 𝜒 ) → ¬ 𝜓 ) )