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	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	biimprd	$$⊢\phi \to \left(\chi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		biimprd.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		id	$$⊢\chi \to \chi$$
3	2 1	syl5ibr	$$⊢\phi \to \left(\chi \to \psi \right)$$