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Theorem omex 4316
 Description: The existence of omega (the class of natural numbers). Axiom 7 of [TakeutiZaring] p. 43. (Contributed by NM, 6-Aug-1994.)
Assertion
Ref Expression
omex

Proof of Theorem omex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 zfinf2 4312 . . 3
2 intexabim 3906 . . 3
31, 2ax-mp 7 . 2
4 dfom3 4315 . . 3
54eleq1i 2103 . 2
63, 5mpbir 134 1
 Colors of variables: wff set class Syntax hints:   wa 97  wex 1381   wcel 1393  cab 2026  wral 2306  cvv 2557  c0 3224  cint 3615   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-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-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-iinf 4311 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-v 2559  df-in 2924  df-ss 2931  df-int 3616  df-iom 4314 This theorem is referenced by:  peano5  4321  omelon  4331  frecex  5981  frecabex  5984  niex  6410  enq0ex  6537  nq0ex  6538  uzenom  9202  frecfzennn  9203  nnenom  9210
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