Theorem biimt

Description: A wff is equivalent to itself with true antecedent. (Contributed by NM, 28-Jan-1996)

	Ref	Expression
Assertion	biimt	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-1	$$⊢\psi \to \left(\phi \to \psi \right)$$
2		pm2.27	$$⊢\phi \to \left(\left(\phi \to \psi \right)\to \psi \right)$$
3	1 2	impbid2	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \to \psi \right)\right)$$