Theorem adantll

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Hypothesis	adant2.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	adantll	$$⊢\left(\left(\theta \wedge \phi \right)\wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		adant2.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2		simpr	$$⊢\left(\theta \wedge \phi \right)\to \phi$$
3	2 1	sylan	$$⊢\left(\left(\theta \wedge \phi \right)\wedge \psi \right)\to \chi$$