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Theorem aisbbisfaisf 41804
Description: Given a is equivalent to b, b is equivalent to there exists a proof for a is equivalent to F. (Contributed by Jarvin Udandy, 30-Aug-2016.)
Hypotheses
Ref Expression
aisbbisfaisf.1 (𝜑𝜓)
aisbbisfaisf.2 (𝜓 ↔ ⊥)
Assertion
Ref Expression
aisbbisfaisf (𝜑 ↔ ⊥)

Proof of Theorem aisbbisfaisf
StepHypRef Expression
1 aisbbisfaisf.1 . 2 (𝜑𝜓)
2 aisbbisfaisf.2 . 2 (𝜓 ↔ ⊥)
31, 2bitri 267 1 (𝜑 ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  wb 198  wfal 1666
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 199
This theorem is referenced by:  mdandysum2p2e4  41901
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