Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdinex1 Structured version   Unicode version

Theorem bdinex1 9284
Description: Bounded version of inex1 3882. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdinex1.bd BOUNDED
bdinex1.1  _V
Assertion
Ref Expression
bdinex1  i^i 
_V

Proof of Theorem bdinex1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bdinex1.1 . . . 4  _V
2 bdinex1.bd . . . . . 6 BOUNDED
32bdeli 9235 . . . . 5 BOUNDED
43bdzfauscl 9278 . . . 4  _V
51, 4ax-mp 7 . . 3
6 dfcleq 2031 . . . . 5  i^i  i^i
7 elin 3120 . . . . . . 7  i^i
87bibi2i 216 . . . . . 6  i^i
98albii 1356 . . . . 5  i^i
106, 9bitri 173 . . . 4  i^i
1110exbii 1493 . . 3  i^i
125, 11mpbir 134 . 2  i^i
1312issetri 2558 1  i^i 
_V
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wal 1240   wceq 1242  wex 1378   wcel 1390   _Vcvv 2551    i^i cin 2910  BOUNDED wbdc 9229
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-bdsep 9273
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-bdc 9230
This theorem is referenced by:  bdinex2  9285  bdinex1g  9286  bdpeano5  9331
  Copyright terms: Public domain W3C validator