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Theorem aistbistaandb 41823
Description: Given a is equivalent to T., also given that b is equivalent to T, there exists a proof for (a and b). (Contributed by Jarvin Udandy, 9-Sep-2016.)
Hypotheses
Ref Expression
aistbistaandb.1 (𝜑 ↔ ⊤)
aistbistaandb.2 (𝜓 ↔ ⊤)
Assertion
Ref Expression
aistbistaandb (𝜑𝜓)

Proof of Theorem aistbistaandb
StepHypRef Expression
1 aistbistaandb.1 . . 3 (𝜑 ↔ ⊤)
21aistia 41810 . 2 𝜑
3 aistbistaandb.2 . . 3 (𝜓 ↔ ⊤)
43aistia 41810 . 2 𝜓
52, 4pm3.2i 463 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: (None)
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