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 ↔ 𝜓 )
Assertion	biimpri	⊢ ( 𝜓 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		biimpri.1	⊢ ( 𝜑 ↔ 𝜓 )
2	1	bicomi	⊢ ( 𝜓 ↔ 𝜑 )
3	2	biimpi	⊢ ( 𝜓 → 𝜑 )