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Theorem bj-bdcel 11071
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 11053 . 2  |- BOUNDED  E. y  e.  x  y  =  A
3 risset 2400 . 2  |-  ( A  e.  x  <->  E. y  e.  x  y  =  A )
42, 3bd0r 11059 1  |- BOUNDED  A  e.  x
Colors of variables: wff set class
Syntax hints:    = wceq 1285    e. wcel 1434   E.wrex 2354  BOUNDED wbd 11046
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468  ax-bd0 11047  ax-bdex 11053
This theorem depends on definitions:  df-bi 115  df-clel 2079  df-rex 2359
This theorem is referenced by:  bj-bd0el  11102  bj-bdsucel  11116
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