Theorem adantl

Description: Inference adding a conjunct to the left of an antecedent. (Contributed by NM, 30-Aug-1993) (Proof shortened by Wolf Lammen, 23-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		adantl.1	$$⊢\phi \to \psi$$
2	1	adantr	$$⊢\left(\phi \wedge \chi \right)\to \psi$$
3	2	ancoms	$$⊢\left(\chi \wedge \phi \right)\to \psi$$