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Theorem bj-bdcel 14986
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 14968 . 2  |- BOUNDED  E. y  e.  x  y  =  A
3 risset 2518 . 2  |-  ( A  e.  x  <->  E. y  e.  x  y  =  A )
42, 3bd0r 14974 1  |- BOUNDED  A  e.  x
Colors of variables: wff set class
Syntax hints:    = wceq 1364    e. wcel 2160   E.wrex 2469  BOUNDED wbd 14961
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545  ax-bd0 14962  ax-bdex 14968
This theorem depends on definitions:  df-bi 117  df-clel 2185  df-rex 2474
This theorem is referenced by:  bj-bd0el  15017  bj-bdsucel  15031
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