Theorem pm4.54

Description: Theorem *4.54 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Nov-2012)

	Ref	Expression
Assertion	pm4.54	⊢ ( ( ¬ 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 ∨ ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		df-an	⊢ ( ( ¬ 𝜑 ∧ 𝜓 ) ↔ ¬ ( ¬ 𝜑 → ¬ 𝜓 ) )
2		pm4.66	⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) ↔ ( 𝜑 ∨ ¬ 𝜓 ) )
3	1 2	xchbinx	⊢ ( ( ¬ 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 ∨ ¬ 𝜓 ) )