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Theorem aiffbbtat 43935
Description: Given a is equivalent to b, b is equivalent to there exists a proof for a is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016.)
Hypotheses
Ref Expression
aiffbbtat.1 (𝜑𝜓)
aiffbbtat.2 (𝜓 ↔ ⊤)
Assertion
Ref Expression
aiffbbtat (𝜑 ↔ ⊤)

Proof of Theorem aiffbbtat
StepHypRef Expression
1 aiffbbtat.1 . 2 (𝜑𝜓)
2 aiffbbtat.2 . 2 (𝜓 ↔ ⊤)
31, 2bitri 278 1 (𝜑 ↔ ⊤)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wtru 1543
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:  dandysum2p2e4  44032  mdandysum2p2e4  44033
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