Theorem anc2l

Description: Conjoin antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994) (Proof shortened by Wolf Lammen, 14-Jul-2013)

	Ref	Expression
Assertion	anc2l	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm5.42	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\leftrightarrow \left(\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)\right)$$
2	1	biimpi	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)\right)$$