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Theorem aibandbiaiaiffb 41568
Description: A closed form showing (a implies b and b implies a) implies (a same-as b). (Contributed by Jarvin Udandy, 3-Sep-2016.)
Assertion
Ref Expression
aibandbiaiaiffb (((𝜑𝜓) ∧ (𝜓𝜑)) → (𝜑𝜓))

Proof of Theorem aibandbiaiaiffb
StepHypRef Expression
1 dfbi2 663 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ (𝜓𝜑)))
21biimpri 218 1 (((𝜑𝜓) ∧ (𝜓𝜑)) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383
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 197  df-an 385
This theorem is referenced by: (None)
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