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Theorem bj-omex2 10102
 Description: Using bounded set induction and the strong axiom of infinity, is a set, that is, we recover ax-infvn 10066 (see bj-2inf 10062 for the equivalence of the latter with bj-omex 10067). (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bj-omex2

Proof of Theorem bj-omex2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-inf2 10101 . . 3
2 vex 2560 . . . 4
3 bdcv 9968 . . . . 5 BOUNDED
43bj-inf2vn 10099 . . . 4
52, 4ax-mp 7 . . 3
61, 5eximii 1493 . 2
76issetri 2564 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wo 629  wal 1241   wceq 1243   wcel 1393  wrex 2307  cvv 2557  c0 3224   csuc 4102  com 4313 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-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-nul 3883  ax-pr 3944  ax-un 4170  ax-bd0 9933  ax-bdim 9934  ax-bdor 9936  ax-bdex 9939  ax-bdeq 9940  ax-bdel 9941  ax-bdsb 9942  ax-bdsep 10004  ax-bdsetind 10093  ax-inf2 10101 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-rab 2315  df-v 2559  df-dif 2920  df-un 2922  df-in 2924  df-ss 2931  df-nul 3225  df-sn 3381  df-pr 3382  df-uni 3581  df-int 3616  df-suc 4108  df-iom 4314  df-bdc 9961  df-bj-ind 10051 This theorem is referenced by: (None)
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