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

Theorem bdeli 10888
Description: Inference associated with bdel 10887. Its converse is bdelir 10889. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdeli.1  |- BOUNDED  A
Assertion
Ref Expression
bdeli  |- BOUNDED  x  e.  A
Distinct variable group:    x, A

Proof of Theorem bdeli
StepHypRef Expression
1 bdeli.1 . 2  |- BOUNDED  A
2 bdel 10887 . 2  |-  (BOUNDED  A  -> BOUNDED  x  e.  A )
31, 2ax-mp 7 1  |- BOUNDED  x  e.  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1434  BOUNDED wbd 10854  BOUNDED wbdc 10882
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-bdc 10883
This theorem is referenced by:  bdph  10892  bdcrab  10894  bdnel  10896  bdccsb  10902  bdcdif  10903  bdcun  10904  bdcin  10905  bdss  10906  bdsnss  10915  bdciun  10920  bdciin  10921  bdinex1  10941  bj-uniex2  10958  bj-inf2vnlem3  11018
  Copyright terms: Public domain W3C validator