Theorem pm4.8

Description: Theorem *4.8 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.8	⊢ ( ( 𝜑 → ¬ 𝜑 ) ↔ ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		pm2.01	⊢ ( ( 𝜑 → ¬ 𝜑 ) → ¬ 𝜑 )
2		ax-1	⊢ ( ¬ 𝜑 → ( 𝜑 → ¬ 𝜑 ) )
3	1 2	impbii	⊢ ( ( 𝜑 → ¬ 𝜑 ) ↔ ¬ 𝜑 )