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

Theorem bdcab 12974
Description: A class defined by class abstraction using a bounded formula is bounded. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdcab.1  |- BOUNDED  ph
Assertion
Ref Expression
bdcab  |- BOUNDED  { x  |  ph }

Proof of Theorem bdcab
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 bdcab.1 . . 3  |- BOUNDED  ph
21bdab 12963 . 2  |- BOUNDED  y  e.  { x  |  ph }
32bdelir 12972 1  |- BOUNDED  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   {cab 2103  BOUNDED wbd 12937  BOUNDED wbdc 12965
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-gen 1410  ax-bd0 12938  ax-bdsb 12947
This theorem depends on definitions:  df-bi 116  df-clab 2104  df-bdc 12966
This theorem is referenced by:  bds  12976  bdcrab  12977  bdccsb  12985  bdcdif  12986  bdcun  12987  bdcin  12988  bdcpw  12994  bdcsn  12995  bdcuni  13001  bdcint  13002  bdciun  13003  bdciin  13004  bdcriota  13008  bj-bdfindis  13072
  Copyright terms: Public domain W3C validator