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Metamath Proof Explorer

Theorem simprbda

Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007)

		Ref	Expression
	Hypothesis	pm3.26bda.1	$⊢ φ \to (ψ \leftrightarrow (χ \land θ))$
	Assertion	simprbda	$⊢ (φ \land ψ) \to χ$

Step	Hyp	Ref	Expression
1		pm3.26bda.1	$⊢ φ \to (ψ \leftrightarrow (χ \land θ))$
2	1	biimpa	$⊢ (φ \land ψ) \to (χ \land θ)$
3	2	simpld	$⊢ (φ \land ψ) \to χ$