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Theorem uunT12p2 31837
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
uunT12p2.1  |-  ( (
ph  /\ T.  /\  ps )  ->  ch )
Assertion
Ref Expression
uunT12p2  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem uunT12p2
StepHypRef Expression
1 3anrot 970 . . . . 5  |-  ( (
ph  /\ T.  /\  ps )  <->  ( T.  /\  ps  /\  ph ) )
2 3anass 969 . . . . 5  |-  ( ( T.  /\  ps  /\  ph )  <->  ( T.  /\  ( ps  /\  ph )
) )
31, 2bitri 249 . . . 4  |-  ( (
ph  /\ T.  /\  ps )  <->  ( T.  /\  ( ps  /\  ph )
) )
4 truan 1387 . . . 4  |-  ( ( T.  /\  ( ps 
/\  ph ) )  <->  ( ps  /\ 
ph ) )
53, 4bitri 249 . . 3  |-  ( (
ph  /\ T.  /\  ps )  <->  ( ps  /\  ph ) )
6 ancom 450 . . 3  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
75, 6bitr4i 252 . 2  |-  ( (
ph  /\ T.  /\  ps )  <->  ( ph  /\  ps ) )
8 uunT12p2.1 . 2  |-  ( (
ph  /\ T.  /\  ps )  ->  ch )
97, 8sylbir 213 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965   T. wtru 1371
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 1373
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator