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Theorem bdinex1 7122
Description: Bounded version of inex1 3865. (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 7073 . . . . 5 BOUNDED
43bdzfauscl 7116 . . . 4  _V
51, 4ax-mp 7 . . 3
6 dfcleq 2016 . . . . 5  i^i  i^i
7 elin 3103 . . . . . . 7  i^i
87bibi2i 216 . . . . . 6  i^i
98albii 1339 . . . . 5  i^i
106, 9bitri 173 . . . 4  i^i
1110exbii 1478 . . 3  i^i
125, 11mpbir 134 . 2  i^i
1312issetri 2542 1  i^i 
_V
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wal 1226   wceq 1228  wex 1362   wcel 1374   _Vcvv 2535    i^i cin 2893  BOUNDED wbdc 7067
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-bdsep 7111
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-in 2901  df-bdc 7068
This theorem is referenced by:  bdinex2  7123  bdinex1g  7124  bdpeano5  7165
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