Metamath Proof Explorer


Theorem ibdr

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

Ref Expression
Hypothesis ibdr.1 ( 𝜑 → ( 𝜒 → ( 𝜓𝜒 ) ) )
Assertion ibdr ( 𝜑 → ( 𝜒𝜓 ) )

Proof

Step Hyp Ref Expression
1 ibdr.1 ( 𝜑 → ( 𝜒 → ( 𝜓𝜒 ) ) )
2 1 bicomdd ( 𝜑 → ( 𝜒 → ( 𝜒𝜓 ) ) )
3 2 ibd ( 𝜑 → ( 𝜒𝜓 ) )