Theorem ibdr

Description: Reverse of ibd . (Contributed by Rodolfo Medina, 30-Sep-2010)

	Ref	Expression
Hypothesis	ibdr.1	⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 ↔ 𝜒 ) ) )
Assertion	ibdr	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		ibdr.1	⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 ↔ 𝜒 ) ) )
2	1	bicomdd	⊢ ( 𝜑 → ( 𝜒 → ( 𝜒 ↔ 𝜓 ) ) )
3	2	ibd	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )