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Theorem elon2 5441
 Description: An ordinal number is an ordinal set. (Contributed by NM, 8-Feb-2004.)
Assertion
Ref Expression
elon2

Proof of Theorem elon2
StepHypRef Expression
1 eloni 5440 . . 3
2 elex 3040 . . 3
31, 2jca 541 . 2
4 elong 5438 . . 3
54biimparc 495 . 2
63, 5impbii 192 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   wcel 1904  cvv 3031   word 5429  con0 5430 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-v 3033  df-in 3397  df-ss 3404  df-uni 4191  df-tr 4491  df-po 4760  df-so 4761  df-fr 4798  df-we 4800  df-ord 5433  df-on 5434 This theorem is referenced by:  sucelon  6663  tfrlem12  7125  tfrlem13  7126  gruina  9261  nobndlem1  30652
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