Theorem adantrrr

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

	Ref	Expression
Hypothesis	adantr2.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
Assertion	adantrrr	$$⊢\left(\phi \wedge \left(\psi \wedge \left(\chi \wedge \tau \right)\right)\right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		adantr2.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
2		simpl	$$⊢\left(\chi \wedge \tau \right)\to \chi$$
3	2 1	sylanr2	$$⊢\left(\phi \wedge \left(\psi \wedge \left(\chi \wedge \tau \right)\right)\right)\to \theta$$