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

Theorem bdelir 11738
Description: Inference associated with df-bdc 11732. Its converse is bdeli 11737. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdelir.1 BOUNDED 𝑥𝐴
Assertion
Ref Expression
bdelir BOUNDED 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bdelir
StepHypRef Expression
1 df-bdc 11732 . 2 (BOUNDED 𝐴 ↔ ∀𝑥BOUNDED 𝑥𝐴)
2 bdelir.1 . 2 BOUNDED 𝑥𝐴
31, 2mpgbir 1387 1 BOUNDED 𝐴
Colors of variables: wff set class
Syntax hints:  wcel 1438  BOUNDED wbd 11703  BOUNDED wbdc 11731
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 11732
This theorem is referenced by:  bdcv  11739  bdcab  11740  bdcvv  11748  bdcnul  11756  bdop  11766
  Copyright terms: Public domain W3C validator