This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem simp2d

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

		Ref	Expression
	Hypothesis	3simp1d.1	$⊢ φ \to (ψ \land χ \land θ)$
	Assertion	simp2d	$⊢ φ \to χ$

Step	Hyp	Ref	Expression
1		3simp1d.1	$⊢ φ \to (ψ \land χ \land θ)$
2		simp2	$⊢ (ψ \land χ \land θ) \to χ$
3	1 2	syl	$⊢ φ \to χ$