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Theorem leweon 7639
 Description: Lexicographical order is a well-ordering of . Proposition 7.56(1) of [TakeutiZaring] p. 54. Note that unlike r0weon 7640, 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:   ,
Allowed substitution hints:   (,)

Proof of Theorem leweon
StepHypRef Expression
1 epweon 4575 . 2
2 leweon.1 . . . 4
3 fvex 5539 . . . . . . . 8
43epelc 4307 . . . . . . 7
5 fvex 5539 . . . . . . . . 9
65epelc 4307 . . . . . . . 8
76anbi2i 675 . . . . . . 7
84, 7orbi12i 507 . . . . . 6
98anbi2i 675 . . . . 5
109opabbii 4083 . . . 4
112, 10eqtr4i 2306 . . 3
1211wexp 6229 . 2
131, 1, 12mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wo 357   wa 358   wceq 1623   wcel 1684   class class class wbr 4023  copab 4076   cep 4303   wwe 4351  con0 4392   cxp 4687  cfv 5255  c1st 6120  c2nd 6121 This theorem is referenced by:  r0weon  7640 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214  ax-un 4512 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-pss 3168  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-tp 3648  df-op 3649  df-uni 3828  df-int 3863  df-br 4024  df-opab 4078  df-mpt 4079  df-tr 4114  df-eprel 4305  df-id 4309  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395  df-on 4396  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fv 5263  df-1st 6122  df-2nd 6123
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