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Theorem leweon 8410
 Description: Lexicographical order is a well-ordering of X. . Proposition 7.56(1) of [TakeutiZaring] p. 54. Note that unlike r0weon 8411, this order is not set-like, as the preimage of is the proper class . (Contributed by Mario Carneiro, 9-Mar-2013.)
Hypothesis
Ref Expression
leweon.1
Assertion
Ref Expression
leweon
Distinct variable group:   ,

Proof of Theorem leweon
StepHypRef Expression
1 epweon 6619 . 2
2 leweon.1 . . . 4
3 fvex 5881 . . . . . . . 8
43epelc 4798 . . . . . . 7
5 fvex 5881 . . . . . . . . 9
65epelc 4798 . . . . . . . 8
76anbi2i 694 . . . . . . 7
84, 7orbi12i 521 . . . . . 6
98anbi2i 694 . . . . 5
109opabbii 4516 . . . 4
112, 10eqtr4i 2489 . . 3
1211wexp 6914 . 2
131, 1, 12mp2an 672 1
 Colors of variables: wff setvar class Syntax hints:  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818   class class class wbr 4452  {copab 4509   cep 4794  Wewwe 4842   con0 4883  X.cxp 5002  `cfv 5593   c1st 6798   c2nd 6799 This theorem is referenced by:  r0weon  8411 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630  ax-pr 4691  ax-un 6592 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-tp 4034  df-op 4036  df-uni 4250  df-int 4287  df-br 4453  df-opab 4511  df-mpt 4512  df-tr 4546  df-eprel 4796  df-id 4800  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fv 5601  df-1st 6800  df-2nd 6801
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