Theorem ancrb

Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999) (Proof shortened by Wolf Lammen, 24-Mar-2013)

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

Proof

Step	Hyp	Ref	Expression
1		iba	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \phi \right)\right)$$
2	1	pm5.74i	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\phi \to \left(\psi \wedge \phi \right)\right)$$