Theorem bianir

Description: A closed form of mpbir , analogous to pm2.27 (assertion). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Roger Witte, 17-Aug-2020)

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

Proof

Step	Hyp	Ref	Expression
1		biimpr	$$⊢\left(\psi \leftrightarrow \phi \right)\to \left(\phi \to \psi \right)$$
2	1	impcom	$$⊢\left(\phi \wedge \left(\psi \leftrightarrow \phi \right)\right)\to \psi$$