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Theorem astbstanbst 37944
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  |-  ( ph  <-> T.  )
astbstanbst.2  |-  ( ps  <-> T.  )
Assertion
Ref Expression
astbstanbst  |-  ( (
ph  /\  ps )  <-> T.  )

Proof of Theorem astbstanbst
StepHypRef Expression
1 astbstanbst.1 . . . 4  |-  ( ph  <-> T.  )
21aistia 37932 . . 3  |-  ph
3 astbstanbst.2 . . . 4  |-  ( ps  <-> T.  )
43aistia 37932 . . 3  |-  ps
52, 4pm3.2i 456 . 2  |-  ( ph  /\ 
ps )
65bitru 1449 1  |-  ( (
ph  /\  ps )  <-> T.  )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    /\ wa 370   T. wtru 1438
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 188  df-an 372  df-tru 1440
This theorem is referenced by:  dandysum2p2e4  38034
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