Theorem anc2li

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994) (Proof shortened by Wolf Lammen, 7-Dec-2012)

	Ref	Expression
Hypothesis	anc2li.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	anc2li	$$⊢\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		anc2li.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		id	$$⊢\phi \to \phi$$
3	1 2	jctild	$$⊢\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)$$