This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem biimpri

Description: Infer a converse implication from a logical equivalence. Inference associated with biimpr . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 16-Sep-2013)

		Ref	Expression
	Hypothesis	biimpri.1	$⊢ φ \leftrightarrow ψ$
	Assertion	biimpri	$⊢ ψ \to φ$

Proof

Step	Hyp	Ref	Expression
1		biimpri.1	$⊢ φ \leftrightarrow ψ$
2	1	bicomi	$⊢ ψ \leftrightarrow φ$
3	2	biimpi	$⊢ ψ \to φ$