Theorem anc2ri

Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994) (Proof shortened by Wolf Lammen, 7-Dec-2012)

	Ref	Expression
Hypothesis	anc2ri.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	anc2ri	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		anc2ri.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		id	$$⊢\phi \to \phi$$
3	1 2	jctird	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \phi \right)\right)$$