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Theorem bdph 13153
 Description: A formula which defines (by class abstraction) a bounded class is bounded. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdph.1 BOUNDED
Assertion
Ref Expression
bdph BOUNDED

Proof of Theorem bdph
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdph.1 . . . . 5 BOUNDED
21bdeli 13149 . . . 4 BOUNDED
3 df-clab 2126 . . . 4
42, 3bd0 13127 . . 3 BOUNDED
54ax-bdsb 13125 . 2 BOUNDED
6 sbid2v 1971 . 2
75, 6bd0 13127 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wcel 1480  wsb 1735  cab 2125  BOUNDED wbd 13115  BOUNDED wbdc 13143 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-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-bd0 13116  ax-bdsb 13125 This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2126  df-bdc 13144 This theorem is referenced by:  bds  13154
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