Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  uunT11p2 Structured version   Unicode version

Theorem uunT11p2 31627
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
uunT11p2.1  |-  ( (
ph  /\  ph  /\ T.  )  ->  ps )
Assertion
Ref Expression
uunT11p2  |-  ( ph  ->  ps )

Proof of Theorem uunT11p2
StepHypRef Expression
1 3anrev 976 . . . 4  |-  ( (
ph  /\  ph  /\ T.  ) 
<->  ( T.  /\  ph  /\ 
ph ) )
2 3anass 969 . . . 4  |-  ( ( T.  /\  ph  /\  ph )  <->  ( T.  /\  ( ph  /\  ph )
) )
3 truan 1386 . . . 4  |-  ( ( T.  /\  ( ph  /\ 
ph ) )  <->  ( ph  /\ 
ph ) )
41, 2, 33bitri 271 . . 3  |-  ( (
ph  /\  ph  /\ T.  ) 
<->  ( ph  /\  ph ) )
5 anidm 644 . . 3  |-  ( (
ph  /\  ph )  <->  ph )
64, 5bitri 249 . 2  |-  ( (
ph  /\  ph  /\ T.  ) 
<-> 
ph )
7 uunT11p2.1 . 2  |-  ( (
ph  /\  ph  /\ T.  )  ->  ps )
86, 7sylbir 213 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965   T. wtru 1370
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 967  df-tru 1372
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator