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

Theorem bdelir 11382
Description: Inference associated with df-bdc 11376. Its converse is bdeli 11381. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdelir.1  |- BOUNDED  x  e.  A
Assertion
Ref Expression
bdelir  |- BOUNDED  A
Distinct variable group:    x, A

Proof of Theorem bdelir
StepHypRef Expression
1 df-bdc 11376 . 2  |-  (BOUNDED  A  <->  A. xBOUNDED  x  e.  A )
2 bdelir.1 . 2  |- BOUNDED  x  e.  A
31, 2mpgbir 1387 1  |- BOUNDED  A
Colors of variables: wff set class
Syntax hints:    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-ia2 105  ax-ia3 106  ax-gen 1383
This theorem depends on definitions:  df-bi 115  df-bdc 11376
This theorem is referenced by:  bdcv  11383  bdcab  11384  bdcvv  11392  bdcnul  11400  bdop  11410
  Copyright terms: Public domain W3C validator