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Theorem peano3 6467
Description: The successor of any natural number is not zero. One of Peano's 5 postulates for arithmetic. Proposition 7.30(3) of [TakeutiZaring] p. 42. (Contributed by NM, 3-Sep-2003.)
Assertion
Ref Expression
peano3

Proof of Theorem peano3
StepHypRef Expression
1 nsuceq0 4770 . 2
21a1i 11 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1749  =/=wne 2585   c0 3614  succsuc 4692   com 6446
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1586  ax-4 1597  ax-5 1661  ax-6 1701  ax-7 1721  ax-10 1768  ax-11 1773  ax-12 1785  ax-13 1934  ax-ext 2403  ax-nul 4396
This theorem depends on definitions:  df-bi 179  df-or 363  df-an 364  df-tru 1355  df-ex 1582  df-nf 1585  df-sb 1694  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2547  df-ne 2587  df-v 2953  df-dif 3308  df-un 3310  df-nul 3615  df-sn 3859  df-suc 4696
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