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Metamath Proof Explorer

Theorem simplbi2

Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011)

		Ref	Expression
	Hypothesis	simplbi2.1	$⊢ φ \leftrightarrow (ψ \land χ)$
	Assertion	simplbi2	$⊢ ψ \to (χ \to φ)$

Step	Hyp	Ref	Expression
1		simplbi2.1	$⊢ φ \leftrightarrow (ψ \land χ)$
2	1	biimpri	$⊢ (ψ \land χ) \to φ$
3	2	ex	$⊢ ψ \to (χ \to φ)$