Theorem biimprcd

Description: Deduce a converse commuted implication from a logical equivalence. (Contributed by NM, 3-May-1994) (Proof shortened by Wolf Lammen, 20-Dec-2013)

	Ref	Expression
Hypothesis	biimpcd.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	biimprcd	$$⊢\chi \to \left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		biimpcd.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		id	$$⊢\chi \to \chi$$
3	2 1	syl5ibrcom	$$⊢\chi \to \left(\phi \to \psi \right)$$