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

Theorem bdinex1 13202
 Description: Bounded version of inex1 4062. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdinex1.bd BOUNDED
bdinex1.1
Assertion
Ref Expression
bdinex1

Proof of Theorem bdinex1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bdinex1.1 . . . 4
2 bdinex1.bd . . . . . 6 BOUNDED
32bdeli 13149 . . . . 5 BOUNDED
43bdzfauscl 13193 . . . 4
51, 4ax-mp 5 . . 3
6 dfcleq 2133 . . . . 5
7 elin 3259 . . . . . . 7
87bibi2i 226 . . . . . 6
98albii 1446 . . . . 5
106, 9bitri 183 . . . 4
1110exbii 1584 . . 3
125, 11mpbir 145 . 2
1312issetri 2695 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104  wal 1329   wceq 1331  wex 1468   wcel 1480  cvv 2686   cin 3070  BOUNDED wbdc 13143 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-bdsep 13187 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-bdc 13144 This theorem is referenced by:  bdinex2  13203  bdinex1g  13204  bdpeano5  13246
 Copyright terms: Public domain W3C validator