Theorem anc2r

Description: Conjoin antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994)

	Ref	Expression
Assertion	anc2r	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \left(\chi \wedge \phi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm3.21	$$⊢\phi \to \left(\chi \to \left(\chi \wedge \phi \right)\right)$$
2	1	imim2d	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \left(\psi \to \left(\chi \wedge \phi \right)\right)\right)$$
3	2	a2i	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \left(\chi \wedge \phi \right)\right)\right)$$