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Theorem hb3or 1457
Description: If  x is not free in  ph,  ps, and  ch, it is not free in  ( ph  \/  ps  \/  ch ). (Contributed by NM, 14-Sep-2003.)
Hypotheses
Ref Expression
hb.1  |-  ( ph  ->  A. x ph )
hb.2  |-  ( ps 
->  A. x ps )
hb.3  |-  ( ch 
->  A. x ch )
Assertion
Ref Expression
hb3or  |-  ( (
ph  \/  ps  \/  ch )  ->  A. x
( ph  \/  ps  \/  ch ) )

Proof of Theorem hb3or
StepHypRef Expression
1 df-3or 897 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
2 hb.1 . . . 4  |-  ( ph  ->  A. x ph )
3 hb.2 . . . 4  |-  ( ps 
->  A. x ps )
42, 3hbor 1454 . . 3  |-  ( (
ph  \/  ps )  ->  A. x ( ph  \/  ps ) )
5 hb.3 . . 3  |-  ( ch 
->  A. x ch )
64, 5hbor 1454 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  A. x ( (
ph  \/  ps )  \/  ch ) )
71, 6hbxfrbi 1377 1  |-  ( (
ph  \/  ps  \/  ch )  ->  A. x
( ph  \/  ps  \/  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 639    \/ w3o 895   A.wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-3or 897
This theorem is referenced by: (None)
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