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Theorem bicomdd 36028
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.)
Hypothesis
Ref Expression
bicomdd.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
bicomdd (𝜑 → (𝜓 → (𝜃𝜒)))

Proof of Theorem bicomdd
StepHypRef Expression
1 bicomdd.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 bicom 225 . 2 ((𝜒𝜃) ↔ (𝜃𝜒))
31, 2syl6ib 254 1 (𝜑 → (𝜓 → (𝜃𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209
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 210
This theorem is referenced by:  ibdr  36032
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