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Theorem uunTT1p2 28620
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
uunTT1p2.1  |-  ( (
ph  /\  T.  /\  T.  )  ->  ps )
Assertion
Ref Expression
uunTT1p2  |-  ( ph  ->  ps )

Proof of Theorem uunTT1p2
StepHypRef Expression
1 3anrot 941 . . . 4  |-  ( (
ph  /\  T.  /\  T.  ) 
<->  (  T.  /\  T.  /\ 
ph ) )
2 3anass 940 . . . 4  |-  ( (  T.  /\  T.  /\  ph )  <->  (  T.  /\  (  T.  /\  ph )
) )
3 anabs5 785 . . . 4  |-  ( (  T.  /\  (  T. 
/\  ph ) )  <->  (  T.  /\ 
ph ) )
41, 2, 33bitri 263 . . 3  |-  ( (
ph  /\  T.  /\  T.  ) 
<->  (  T.  /\  ph ) )
5 truan 1337 . . 3  |-  ( (  T.  /\  ph )  <->  ph )
64, 5bitri 241 . 2  |-  ( (
ph  /\  T.  /\  T.  ) 
<-> 
ph )
7 uunTT1p2.1 . 2  |-  ( (
ph  /\  T.  /\  T.  )  ->  ps )
86, 7sylbir 205 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936    T. wtru 1322
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 178  df-an 361  df-3an 938  df-tru 1325
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