Theorem simp2d

Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005)

	Ref	Expression
Hypothesis	3simp1d.1	$$⊢\phi \to \left(\psi \wedge \chi \wedge \theta \right)$$
Assertion	simp2d	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		3simp1d.1	$$⊢\phi \to \left(\psi \wedge \chi \wedge \theta \right)$$
2		simp2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \chi$$
3	1 2	syl	$$⊢\phi \to \chi$$