Theorem ancld

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994) (Proof shortened by Wolf Lammen, 1-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		ancld.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		idd	$$⊢\phi \to \left(\psi \to \psi \right)$$
3	2 1	jcad	$$⊢\phi \to \left(\psi \to \left(\psi \wedge \chi \right)\right)$$