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

Theorem bdel 11380
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 11376 . 2  |-  (BOUNDED  A  <->  A. xBOUNDED  x  e.  A )
2 sp 1446 . 2  |-  ( A. xBOUNDED  x  e.  A  -> BOUNDED  x  e.  A )
31, 2sylbi 119 1  |-  (BOUNDED  A  -> BOUNDED  x  e.  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287    e. wcel 1438  BOUNDED wbd 11347  BOUNDED wbdc 11375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1445
This theorem depends on definitions:  df-bi 115  df-bdc 11376
This theorem is referenced by:  bdeli  11381
  Copyright terms: Public domain W3C validator