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Theorem bdel 13073
Description: The belonging of a setvar in a bounded class is a bounded formula. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdel  |-  (BOUNDED  A  -> BOUNDED  x  e.  A )
Distinct variable group:    x, A

Proof of Theorem bdel
StepHypRef Expression
1 df-bdc 13069 . 2  |-  (BOUNDED  A  <->  A. xBOUNDED  x  e.  A )
2 sp 1488 . 2  |-  ( A. xBOUNDED  x  e.  A  -> BOUNDED  x  e.  A )
31, 2sylbi 120 1  |-  (BOUNDED  A  -> BOUNDED  x  e.  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1329    e. wcel 1480  BOUNDED wbd 13040  BOUNDED wbdc 13068
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1487
This theorem depends on definitions:  df-bi 116  df-bdc 13069
This theorem is referenced by:  bdeli  13074
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