Theorem pm4.52

Description: Theorem *4.52 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Nov-2012)

	Ref	Expression
Assertion	pm4.52	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( ¬ 𝜑 ∨ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		annim	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( 𝜑 → 𝜓 ) )
2		imor	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( ¬ 𝜑 ∨ 𝜓 ) )
3	1 2	xchbinx	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( ¬ 𝜑 ∨ 𝜓 ) )