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Theorem aistia 41704
Description: Given a is equivalent to , there exists a proof for a. (Contributed by Jarvin Udandy, 30-Aug-2016.)
Hypothesis
Ref Expression
aistia.1 (𝜑 ↔ ⊤)
Assertion
Ref Expression
aistia 𝜑

Proof of Theorem aistia
StepHypRef Expression
1 aistia.1 . 2 (𝜑 ↔ ⊤)
2 tbtru 1661 . 2 (𝜑 ↔ (𝜑 ↔ ⊤))
31, 2mpbir 222 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wb 197  wtru 1653
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 198  df-tru 1656
This theorem is referenced by:  astbstanbst  41716  aistbistaandb  41717  aistbisfiaxb  41726  aisfbistiaxb  41727  aifftbifffaibif  41728  aifftbifffaibifff  41729  dandysum2p2e4  41805
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