Theorem adantlrl

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

	Ref	Expression
Hypothesis	adantl2.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	adantlrl	$$⊢\left(\left(\phi \wedge \left(\tau \wedge \psi \right)\right)\wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		adantl2.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
2		simpr	$$⊢\left(\tau \wedge \psi \right)\to \psi$$
3	2 1	sylanl2	$$⊢\left(\left(\phi \wedge \left(\tau \wedge \psi \right)\right)\wedge \chi \right)\to \theta$$