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Metamath Proof Explorer

Theorem simp2bi

Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

		Ref	Expression
	Hypothesis	3simp1bi.1	$⊢ φ \leftrightarrow (ψ \land χ \land θ)$
	Assertion	simp2bi	$⊢ φ \to χ$

Step	Hyp	Ref	Expression
1		3simp1bi.1	$⊢ φ \leftrightarrow (ψ \land χ \land θ)$
2	1	biimpi	$⊢ φ \to (ψ \land χ \land θ)$
3	2	simp2d	$⊢ φ \to χ$