Theorem ibdr 38859

Description: Reverse of ibd 269. (Contributed by Rodolfo Medina, 30-Sep-2010.)

Hypothesis

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

Assertion

Ref	Expression
ibdr	⊢ (𝜑 → (𝜒 → 𝜓))

Proof of Theorem ibdr

Step	Hyp	Ref	Expression
1		ibdr.1	. . 3 ⊢ (𝜑 → (𝜒 → (𝜓 ↔ 𝜒)))
2	1	bicomdd 38855	. 2 ⊢ (𝜑 → (𝜒 → (𝜒 ↔ 𝜓)))
3	2	ibd 269	1 ⊢ (𝜑 → (𝜒 → 𝜓))

Syntax hints:   → wi 4   ↔ wb 206

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207

This theorem is referenced by: (None)