Theorem 3adantl2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Hypothesis	3adantl.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	3adantl2	$$⊢\left(\left(\phi \wedge \tau \wedge \psi \right)\wedge \chi \right)\to \theta$$

Proof

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