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Metamath Proof Explorer

Theorem simprbi

Description: Deduction eliminating a conjunct. (Contributed by NM, 27-May-1998)

		Ref	Expression
	Hypothesis	simprbi.1	$⊢ φ \leftrightarrow (ψ \land χ)$
	Assertion	simprbi	$⊢ φ \to χ$

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