Theorem pm4.15

Description: Theorem *4.15 of WhiteheadRussell p. 117. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 18-Nov-2012)

	Ref	Expression
Assertion	pm4.15	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) → ¬ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		con2b	⊢ ( ( ( 𝜓 ∧ 𝜒 ) → ¬ 𝜑 ) ↔ ( 𝜑 → ¬ ( 𝜓 ∧ 𝜒 ) ) )
2		nan	⊢ ( ( 𝜑 → ¬ ( 𝜓 ∧ 𝜒 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 ) )
3	1 2	bitr2i	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) → ¬ 𝜑 ) )