Theorem ad3antrrr

Description: Deduction adding three conjuncts to antecedent. (Contributed by NM, 28-Jul-2012)

	Ref	Expression
Hypothesis	ad2ant.1	$$⊢\phi \to \psi$$
Assertion	ad3antrrr	$$⊢\left(\left(\left(\phi \wedge \chi \right)\wedge \theta \right)\wedge \tau \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		ad2ant.1	$$⊢\phi \to \psi$$
2	1	adantr	$$⊢\left(\phi \wedge \chi \right)\to \psi$$
3	2	ad2antrr	$$⊢\left(\left(\left(\phi \wedge \chi \right)\wedge \theta \right)\wedge \tau \right)\to \psi$$