Theorem anclb

Description: Conjoin antecedent to left of consequent. Theorem *4.7 of WhiteheadRussell p. 120. (Contributed by NM, 25-Jul-1999) (Proof shortened by Wolf Lammen, 24-Mar-2013)

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

Proof

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