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Theorem bdcdif 13048
 Description: The difference of two bounded classes is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bdcdif.1 BOUNDED
bdcdif.2 BOUNDED
Assertion
Ref Expression
bdcdif BOUNDED

Proof of Theorem bdcdif
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcdif.1 . . . . 5 BOUNDED
21bdeli 13033 . . . 4 BOUNDED
3 bdcdif.2 . . . . . 6 BOUNDED
43bdeli 13033 . . . . 5 BOUNDED
54ax-bdn 13004 . . . 4 BOUNDED
62, 5ax-bdan 13002 . . 3 BOUNDED
76bdcab 13036 . 2 BOUNDED
8 df-dif 3068 . 2
97, 8bdceqir 13031 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wn 3   wa 103   wcel 1480  cab 2123   cdif 3063  BOUNDED wbdc 13027 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2119  ax-bd0 13000  ax-bdan 13002  ax-bdn 13004  ax-bdsb 13009 This theorem depends on definitions:  df-bi 116  df-clab 2124  df-cleq 2130  df-clel 2133  df-dif 3068  df-bdc 13028 This theorem is referenced by:  bdcnulALT  13053
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