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Theorem hbn 1665
Description: If  x is not free in  ph, it is not free in  -.  ph. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbn.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
hbn  |-  ( -. 
ph  ->  A. x  -.  ph )

Proof of Theorem hbn
StepHypRef Expression
1 hbnt 1664 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( -.  ph  ->  A. x  -.  ph )
)
2 hbn.1 . 2  |-  ( ph  ->  A. x ph )
31, 2mpg 1462 1  |-  ( -. 
ph  ->  A. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1362
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1458  ax-gen 1460  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370
This theorem is referenced by:  hbnae  1732  sbn  1964  euor  2064  euor2  2096
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