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Theorem leweon 7523
 Description: Lexicographical order is a well-ordering of . Proposition 7.56(1) of [TakeutiZaring] p. 54. Note that unlike r0weon 7524, 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 4466 . 2
2 leweon.1 . . . 4
3 fvex 5391 . . . . . . . 8
43epelc 4200 . . . . . . 7
5 fvex 5391 . . . . . . . . 9
65epelc 4200 . . . . . . . 8
76anbi2i 678 . . . . . . 7
84, 7orbi12i 509 . . . . . 6
98anbi2i 678 . . . . 5
109opabbii 3980 . . . 4
112, 10eqtr4i 2276 . . 3
1211wexp 6081 . 2
131, 1, 12mp2an 656 1
 Colors of variables: wff set class Syntax hints:   wo 359   wa 360   wceq 1619   wcel 1621   class class class wbr 3920  copab 3973   cep 4196   wwe 4244  con0 4285   cxp 4578  cfv 4592  c1st 5972  c2nd 5973 This theorem is referenced by:  r0weon  7524 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-rab 2516  df-v 2729  df-sbc 2922  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-pss 3091  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-tp 3552  df-op 3553  df-uni 3728  df-int 3761  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-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-fv 4608  df-1st 5974  df-2nd 5975
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