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Theorem simplbi2comt 655
Description: Closed form of simplbi2com 656. (Contributed by Alan Sare, 22-Jul-2012.)
Assertion
Ref Expression
simplbi2comt ((𝜑 ↔ (𝜓𝜒)) → (𝜒 → (𝜓𝜑)))

Proof of Theorem simplbi2comt
StepHypRef Expression
1 biimpr 210 . 2 ((𝜑 ↔ (𝜓𝜒)) → ((𝜓𝜒) → 𝜑))
21expcomd 453 1 ((𝜑 ↔ (𝜓𝜒)) → (𝜒 → (𝜓𝜑)))
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:  2uasbanhVD  39461
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