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Theorem leweon 7931
 Description: Lexicographical order is a well-ordering of . Proposition 7.56(1) of [TakeutiZaring] p. 54. Note that unlike r0weon 7932, 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 4799 . 2
2 leweon.1 . . . 4
3 fvex 5773 . . . . . . . 8
43epelc 4531 . . . . . . 7
5 fvex 5773 . . . . . . . . 9
65epelc 4531 . . . . . . . 8
76anbi2i 677 . . . . . . 7
84, 7orbi12i 509 . . . . . 6
98anbi2i 677 . . . . 5
109opabbii 4303 . . . 4
112, 10eqtr4i 2466 . . 3
1211wexp 6496 . 2
131, 1, 12mp2an 655 1
 Colors of variables: wff set class Syntax hints:   wo 359   wa 360   wceq 1654   wcel 1728   class class class wbr 4243  copab 4296   cep 4527   wwe 4575  con0 4616   cxp 4911  cfv 5489  c1st 6383  c2nd 6384 This theorem is referenced by:  r0weon  7932 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-13 1730  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4361  ax-nul 4369  ax-pow 4412  ax-pr 4438  ax-un 4736 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rex 2718  df-rab 2721  df-v 2967  df-sbc 3171  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-pss 3325  df-nul 3617  df-if 3768  df-sn 3849  df-pr 3850  df-tp 3851  df-op 3852  df-uni 4045  df-int 4080  df-br 4244  df-opab 4298  df-mpt 4299  df-tr 4334  df-eprel 4529  df-id 4533  df-po 4538  df-so 4539  df-fr 4576  df-we 4578  df-ord 4619  df-on 4620  df-xp 4919  df-rel 4920  df-cnv 4921  df-co 4922  df-dm 4923  df-rn 4924  df-res 4925  df-ima 4926  df-iota 5453  df-fun 5491  df-fv 5497  df-1st 6385  df-2nd 6386
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