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Theorem uunTT1p1 28968
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
uunTT1p1.1  |-  ( (  T.  /\  ph  /\  T.  )  ->  ps )
Assertion
Ref Expression
uunTT1p1  |-  ( ph  ->  ps )

Proof of Theorem uunTT1p1
StepHypRef Expression
1 3ancomb 946 . . . 4  |-  ( (  T.  /\  ph  /\  T.  )  <->  (  T.  /\  T.  /\  ph ) )
2 3anass 941 . . . 4  |-  ( (  T.  /\  T.  /\  ph )  <->  (  T.  /\  (  T.  /\  ph )
) )
3 anabs5 786 . . . 4  |-  ( (  T.  /\  (  T. 
/\  ph ) )  <->  (  T.  /\ 
ph ) )
41, 2, 33bitri 264 . . 3  |-  ( (  T.  /\  ph  /\  T.  )  <->  (  T.  /\  ph ) )
5 truan 1341 . . 3  |-  ( (  T.  /\  ph )  <->  ph )
64, 5bitri 242 . 2  |-  ( (  T.  /\  ph  /\  T.  )  <->  ph )
7 uunTT1p1.1 . 2  |-  ( (  T.  /\  ph  /\  T.  )  ->  ps )
86, 7sylbir 206 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937    T. wtru 1326
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 179  df-an 362  df-3an 939  df-tru 1329
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