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Metamath Proof Explorer

Theorem pm4.81

Description: A formula is equivalent to its negation implying it. Theorem *4.81 of WhiteheadRussell p. 122. Note that the second step, using pm2.24 , could also use ax-1 . (Contributed by NM, 3-Jan-2005)

		Ref	Expression
	Assertion	pm4.81	⊢ ( ( ¬ 𝜑 → 𝜑 ) ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		pm2.18	⊢ ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 )
2		pm2.24	⊢ ( 𝜑 → ( ¬ 𝜑 → 𝜑 ) )
3	1 2	impbii	⊢ ( ( ¬ 𝜑 → 𝜑 ) ↔ 𝜑 )