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Theorem astbstanbst 41822
Description: Given a is equivalent to T., also given that b is equivalent to T, there exists a proof for a and b is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016.)
Hypotheses
Ref Expression
astbstanbst.1 (𝜑 ↔ ⊤)
astbstanbst.2 (𝜓 ↔ ⊤)
Assertion
Ref Expression
astbstanbst ((𝜑𝜓) ↔ ⊤)

Proof of Theorem astbstanbst
StepHypRef Expression
1 astbstanbst.1 . . . 4 (𝜑 ↔ ⊤)
21aistia 41810 . . 3 𝜑
3 astbstanbst.2 . . . 4 (𝜓 ↔ ⊤)
43aistia 41810 . . 3 𝜓
52, 4pm3.2i 463 . 2 (𝜑𝜓)
65bitru 1663 1 ((𝜑𝜓) ↔ ⊤)
Colors of variables: wff setvar class
Syntax hints:  wb 198  wa 385  wtru 1654
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  df-an 386  df-tru 1657
This theorem is referenced by:  dandysum2p2e4  41911
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