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Metamath Proof Explorer

Theorem biimprd

Description: Deduce a converse implication from a logical equivalence. Deduction associated with biimpr and biimpri . (Contributed by NM, 11-Jan-1993) (Proof shortened by Wolf Lammen, 22-Sep-2013)

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

Proof

Step	Hyp	Ref	Expression
1		biimprd.1	$⊢ φ \to (ψ \leftrightarrow χ)$
2		id	$⊢ χ \to χ$
3	2 1	imbitrrid	$⊢ φ \to (χ \to ψ)$