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Theorem bj-bdcel 11216
Description: Boundedness of a membership formula. (Contributed by BJ, 8-Dec-2019.)
Hypothesis
Ref Expression
bj-bdcel.bd  |- BOUNDED  y  =  A
Assertion
Ref Expression
bj-bdcel  |- BOUNDED  A  e.  x
Distinct variable groups:    x, y    y, A
Allowed substitution hint:    A( x)

Proof of Theorem bj-bdcel
StepHypRef Expression
1 bj-bdcel.bd . . 3  |- BOUNDED  y  =  A
21ax-bdex 11198 . 2  |- BOUNDED  E. y  e.  x  y  =  A
3 risset 2402 . 2  |-  ( A  e.  x  <->  E. y  e.  x  y  =  A )
42, 3bd0r 11204 1  |- BOUNDED  A  e.  x
Colors of variables: wff set class
Syntax hints:    = wceq 1287    e. wcel 1436   E.wrex 2356  BOUNDED wbd 11191
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-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470  ax-bd0 11192  ax-bdex 11198
This theorem depends on definitions:  df-bi 115  df-clel 2081  df-rex 2361
This theorem is referenced by:  bj-bd0el  11247  bj-bdsucel  11261
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