Metamath Proof Explorer


Theorem bicomdd

Description: Commute two sides of a biconditional in a deduction. (Contributed by Rodolfo Medina, 19-Oct-2010) (Proof shortened by Andrew Salmon, 29-Jun-2011)

Ref Expression
Hypothesis bicomdd.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
Assertion bicomdd ( 𝜑 → ( 𝜓 → ( 𝜃𝜒 ) ) )

Proof

Step Hyp Ref Expression
1 bicomdd.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
2 bicom ( ( 𝜒𝜃 ) ↔ ( 𝜃𝜒 ) )
3 1 2 syl6ib ( 𝜑 → ( 𝜓 → ( 𝜃𝜒 ) ) )