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Theorem fzval 11728
 Description: The value of a finite set of sequential integers. E.g., means the set . A special case of this definition (starting at 1) appears as Definition 11-2.1 of [Gleason] p. 141, where _k means our ; he calls these sets segments of the integers. (Contributed by NM, 6-Sep-2005.) (Revised by Mario Carneiro, 3-Nov-2013.)
Assertion
Ref Expression
fzval
Distinct variable groups:   ,   ,

Proof of Theorem fzval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 breq1 4398 . . . 4
21anbi1d 703 . . 3
32rabbidv 3051 . 2
4 breq2 4399 . . . 4
54anbi2d 702 . . 3
65rabbidv 3051 . 2
7 df-fz 11727 . 2
8 zex 10914 . . 3
98rabex 4545 . 2
103, 6, 7, 9ovmpt2 6419 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 367   wceq 1405   wcel 1842  crab 2758   class class class wbr 4395  (class class class)co 6278   cle 9659  cz 10905  cfz 11726 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630  ax-cnex 9578  ax-resscn 9579 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3or 975  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rab 2763  df-v 3061  df-sbc 3278  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-br 4396  df-opab 4454  df-id 4738  df-xp 4829  df-rel 4830  df-cnv 4831  df-co 4832  df-dm 4833  df-iota 5533  df-fun 5571  df-fv 5577  df-ov 6281  df-oprab 6282  df-mpt2 6283  df-neg 9844  df-z 10906  df-fz 11727 This theorem is referenced by:  fzval2  11729  elfz1  11731
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