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Theorem om2uz0i 10888
 Description: The mapping is a one-to-one mapping from onto upper integers that will be used to construct a recursive definition generator. Ordinal natural number 0 maps to complex number (normally 0 for the upper integers or 1 for the upper integers ), 1 maps to + 1, etc. This theorem shows the value of at ordinal natural number zero. (This series of theorems generalizes an earlier series for contributed by Raph Levien, 10-Apr-2004.) (Contributed by NM, 3-Oct-2004.) (Revised by Mario Carneiro, 13-Sep-2013.)
Hypotheses
Ref Expression
om2uz.1
om2uz.2
Assertion
Ref Expression
om2uz0i
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem om2uz0i
StepHypRef Expression
1 om2uz.2 . . 3
21fveq1i 5378 . 2
3 om2uz.1 . . 3
4 fr0g 6334 . . 3
53, 4ax-mp 10 . 2
62, 5eqtri 2273 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   wcel 1621  cvv 2727  c0 3362   cmpt 3974  com 4547   cres 4582  cfv 4592  (class class class)co 5710  crdg 6308  c1 8618   caddc 8620  cz 9903 This theorem is referenced by:  om2uzuzi  10890  om2uzrani  10893  om2uzrdg  10897  uzrdgxfr  10907  fzennn  10908  axdc4uzlem  10922  hashgadd  11237 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-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108  ax-un 4403 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 940  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-reu 2515  df-rab 2516  df-v 2729  df-sbc 2922  df-csb 3010  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-pss 3091  df-nul 3363  df-if 3471  df-pw 3532  df-sn 3550  df-pr 3551  df-tp 3552  df-op 3553  df-uni 3728  df-iun 3805  df-br 3921  df-opab 3975  df-mpt 3976  df-tr 4011  df-eprel 4198  df-id 4202  df-po 4207  df-so 4208  df-fr 4245  df-we 4247  df-ord 4288  df-on 4289  df-lim 4290  df-suc 4291  df-om 4548  df-xp 4594  df-rel 4595  df-cnv 4596  df-co 4597  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fun 4602  df-fn 4603  df-f 4604  df-f1 4605  df-fo 4606  df-f1o 4607  df-fv 4608  df-recs 6274  df-rdg 6309
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