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Theorem bj-omex 7164
 Description: Proof of omex 4243 from ax-infvn 7163. (Contributed by BJ, 14-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-omex 𝜔 V

Proof of Theorem bj-omex
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-infvn 7163 . 2 x(Ind x y(Ind yxy))
2 bj-2inf 7160 . 2 (𝜔 V ↔ x(Ind x y(Ind yxy)))
31, 2mpbir 134 1 𝜔 V
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97  ∀wal 1226  ∃wex 1362   ∈ wcel 1374  Vcvv 2535   ⊆ wss 2894  𝜔com 4240  Ind wind 7149 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 532  ax-in2 533  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-13 1385  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-nul 3857  ax-pr 3918  ax-un 4120  ax-bd0 7040  ax-bdor 7043  ax-bdex 7046  ax-bdeq 7047  ax-bdel 7048  ax-bdsb 7049  ax-bdsep 7111  ax-infvn 7163 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-ral 2289  df-rex 2290  df-rab 2293  df-v 2537  df-dif 2897  df-un 2899  df-in 2901  df-ss 2908  df-nul 3202  df-sn 3356  df-pr 3357  df-uni 3555  df-int 3590  df-suc 4057  df-iom 4241  df-bdc 7068  df-bj-ind 7150 This theorem is referenced by:  bdpeano5  7165  speano5  7166  bdfind  7168  bj-omtrans  7178  bj-omelon  7181
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