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Theorem bdne 11390
Description: Inequality of two setvars is a bounded formula. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdne  |- BOUNDED  x  =/=  y

Proof of Theorem bdne
StepHypRef Expression
1 ax-bdeq 11357 . . 3  |- BOUNDED  x  =  y
21ax-bdn 11354 . 2  |- BOUNDED  -.  x  =  y
3 df-ne 2256 . 2  |-  ( x  =/=  y  <->  -.  x  =  y )
42, 3bd0r 11362 1  |- BOUNDED  x  =/=  y
Colors of variables: wff set class
Syntax hints:   -. wn 3    =/= wne 2255  BOUNDED wbd 11349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11350  ax-bdn 11354  ax-bdeq 11357
This theorem depends on definitions:  df-bi 115  df-ne 2256
This theorem is referenced by: (None)
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