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Theorem bisym 214
Description: Express symmetries of theorems in terms of biconditionals. (Contributed by Wolf Lammen, 14-May-2013.)
Assertion
Ref Expression
bisym (((𝜑𝜓) → (𝜒𝜃)) → (((𝜓𝜑) → (𝜃𝜒)) → ((𝜑𝜓) → (𝜒𝜃))))

Proof of Theorem bisym
StepHypRef Expression
1 bi3 112 . 2 ((𝜒𝜃) → ((𝜃𝜒) → (𝜒𝜃)))
21bi3ant 213 1 (((𝜑𝜓) → (𝜒𝜃)) → (((𝜓𝜑) → (𝜃𝜒)) → ((𝜑𝜓) → (𝜒𝜃))))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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