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Theorem bothtbothsame 27867
Description: Given both a,b are equivalent to T., there exists a proof for a is the same as b. (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
bothtbothsame.1  |-  ( ph  <->  T.  )
bothtbothsame.2  |-  ( ps  <->  T.  )
Assertion
Ref Expression
bothtbothsame  |-  ( ph  <->  ps )

Proof of Theorem bothtbothsame
StepHypRef Expression
1 bothtbothsame.1 . . . 4  |-  ( ph  <->  T.  )
21aistia 27865 . . 3  |-  ph
3 bothtbothsame.2 . . . 4  |-  ( ps  <->  T.  )
43aistia 27865 . . 3  |-  ps
52, 4pm3.2i 441 . 2  |-  ( ph  /\ 
ps )
6 pm5.1 830 . 2  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)
75, 6ax-mp 8 1  |-  ( ph  <->  ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    T. wtru 1307
This theorem is referenced by:  mdandyv1  27895  mdandyv2  27896  mdandyv3  27897  mdandyv4  27898  mdandyv5  27899  mdandyv6  27900  mdandyv7  27901  mdandyv8  27902  mdandyv9  27903  mdandyv10  27904  mdandyv11  27905  mdandyv12  27906  mdandyv13  27907  mdandyv14  27908  mdandyv15  27909  dandysum2p2e4  27943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310
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