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Theorem fnwe 6465
 Description: A variant on lexicographic order, which sorts first by some function of the base set, and then by a "backup" well-ordering when the function value is equal on both elements. (Contributed by Mario Carneiro, 10-Mar-2013.) (Revised by Mario Carneiro, 18-Nov-2014.)
Hypotheses
Ref Expression
fnwe.1
fnwe.2
fnwe.3
fnwe.4
fnwe.5
Assertion
Ref Expression
fnwe
Distinct variable groups:   ,,,   ,,,   ,,   ,,,   ,,,   ,,,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem fnwe
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fnwe.1 . 2
2 fnwe.2 . 2
3 fnwe.3 . 2
4 fnwe.4 . 2
5 fnwe.5 . 2
6 eqid 2438 . 2
7 eqid 2438 . 2
81, 2, 3, 4, 5, 6, 7fnwelem 6464 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360   wceq 1653   wcel 1726  cvv 2958  cop 3819   class class class wbr 4215  copab 4268   cmpt 4269   wwe 4543   cxp 4879  cima 4884  wf 5453  cfv 5457  c1st 6350  c2nd 6351 This theorem is referenced by:  r0weon  7899 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 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704 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 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-int 4053  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-isom 5466  df-1st 6352  df-2nd 6353
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