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	$$⊢\left(\neg \phi \to \phi \right)\leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.18	$$⊢\left(\neg \phi \to \phi \right)\to \phi$$
2		pm2.24	$$⊢\phi \to \left(\neg \phi \to \phi \right)$$
3	1 2	impbii	$$⊢\left(\neg \phi \to \phi \right)\leftrightarrow \phi$$