Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  uunT12p4 Structured version   Unicode version

Theorem uunT12p4 34013
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
uunT12p4.1  |-  ( (
ph  /\  ps  /\ T.  )  ->  ch )
Assertion
Ref Expression
uunT12p4  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem uunT12p4
StepHypRef Expression
1 3anrot 976 . . . 4  |-  ( ( T.  /\  ph  /\  ps )  <->  ( ph  /\  ps  /\ T.  ) )
2 3anass 975 . . . 4  |-  ( ( T.  /\  ph  /\  ps )  <->  ( T.  /\  ( ph  /\  ps )
) )
31, 2bitr3i 251 . . 3  |-  ( (
ph  /\  ps  /\ T.  ) 
<->  ( T.  /\  ( ph  /\  ps ) ) )
4 truan 1415 . . 3  |-  ( ( T.  /\  ( ph  /\ 
ps ) )  <->  ( ph  /\ 
ps ) )
53, 4bitri 249 . 2  |-  ( (
ph  /\  ps  /\ T.  ) 
<->  ( ph  /\  ps ) )
6 uunT12p4.1 . 2  |-  ( (
ph  /\  ps  /\ T.  )  ->  ch )
75, 6sylbir 213 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367    /\ w3a 971   T. wtru 1399
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 369  df-3an 973  df-tru 1401
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator