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Theorem zfinf2 7227
 Description: A standard version of the Axiom of Infinity, using definitions to abbreviate. Axiom Inf of [BellMachover] p. 472. (See ax-inf2 7226 for the unabbreviated version.) (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
zfinf2
Distinct variable group:   ,

Proof of Theorem zfinf2
StepHypRef Expression
1 ax-inf2 7226 . 2
2 0el 3378 . . . . 5
3 df-rex 2514 . . . . 5
42, 3bitri 242 . . . 4
5 sucel 4358 . . . . . . 7
6 df-rex 2514 . . . . . . 7
75, 6bitri 242 . . . . . 6
87ralbii 2531 . . . . 5
9 df-ral 2513 . . . . 5
108, 9bitri 242 . . . 4
114, 10anbi12i 681 . . 3
1211exbii 1580 . 2
131, 12mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178   wo 359   wa 360  wal 1532  wex 1537   wceq 1619   wcel 1621  wral 2509  wrex 2510  c0 3362   csuc 4287 This theorem is referenced by:  omex  7228 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-inf2 7226 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-v 2729  df-dif 3081  df-un 3083  df-nul 3363  df-sn 3550  df-suc 4291
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