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

Theorem bdssexi 13678
Description: Bounded version of ssexi 4117. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdssexi.bd  |- BOUNDED  A
bdssexi.1  |-  B  e. 
_V
bdssexi.2  |-  A  C_  B
Assertion
Ref Expression
bdssexi  |-  A  e. 
_V

Proof of Theorem bdssexi
StepHypRef Expression
1 bdssexi.2 . 2  |-  A  C_  B
2 bdssexi.bd . . 3  |- BOUNDED  A
3 bdssexi.1 . . 3  |-  B  e. 
_V
42, 3bdssex 13677 . 2  |-  ( A 
C_  B  ->  A  e.  _V )
51, 4ax-mp 5 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 2135   _Vcvv 2724    C_ wss 3114  BOUNDED wbdc 13615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146  ax-bdsep 13659
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-v 2726  df-in 3120  df-ss 3127  df-bdc 13616
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator