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Theorem uunTT1p1 31361
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 969 . . . 4  |-  ( ( T.  /\  ph  /\ T.  )  <->  ( T.  /\ T.  /\  ph ) )
2 3anass 964 . . . 4  |-  ( ( T.  /\ T.  /\  ph )  <->  ( T.  /\  ( T.  /\  ph )
) )
3 anabs5 802 . . . 4  |-  ( ( T.  /\  ( T. 
/\  ph ) )  <->  ( T.  /\  ph ) )
41, 2, 33bitri 271 . . 3  |-  ( ( T.  /\  ph  /\ T.  )  <->  ( T.  /\  ph ) )
5 truan 1381 . . 3  |-  ( ( T.  /\  ph )  <->  ph )
64, 5bitri 249 . 2  |-  ( ( T.  /\  ph  /\ T.  )  <->  ph )
7 uunTT1p1.1 . 2  |-  ( ( T.  /\  ph  /\ T.  )  ->  ps )
86, 7sylbir 213 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 960   T. wtru 1365
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 185  df-an 371  df-3an 962  df-tru 1367
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator