Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdcrab Unicode version

Theorem bdcrab 13155
 Description: A class defined by restricted abstraction from a bounded class and a bounded formula is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bdcrab.1 BOUNDED
bdcrab.2 BOUNDED
Assertion
Ref Expression
bdcrab BOUNDED
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem bdcrab
StepHypRef Expression
1 bdcrab.1 . . . . 5 BOUNDED
21bdeli 13149 . . . 4 BOUNDED
3 bdcrab.2 . . . 4 BOUNDED
42, 3ax-bdan 13118 . . 3 BOUNDED
54bdcab 13152 . 2 BOUNDED
6 df-rab 2425 . 2
75, 6bdceqir 13147 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wa 103   wcel 1480  cab 2125  crab 2420  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-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121  ax-bd0 13116  ax-bdan 13118  ax-bdsb 13125 This theorem depends on definitions:  df-bi 116  df-clab 2126  df-cleq 2132  df-clel 2135  df-rab 2425  df-bdc 13144 This theorem is referenced by:  bdrabexg  13209
 Copyright terms: Public domain W3C validator