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Theorem fzval 11005
 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 4179 . . . 4
21anbi1d 686 . . 3
32rabbidv 2912 . 2
4 breq2 4180 . . . 4
54anbi2d 685 . . 3
65rabbidv 2912 . 2
7 df-fz 11004 . 2
8 zex 10251 . . 3
98rabex 4318 . 2
103, 6, 7, 9ovmpt2 6172 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1649   wcel 1721  crab 2674   class class class wbr 4176  (class class class)co 6044   cle 9081  cz 10242  cfz 11003 This theorem is referenced by:  fzval2  11006  elfz1  11008 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-sep 4294  ax-nul 4302  ax-pr 4367  ax-cnex 9006  ax-resscn 9007 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262  df-mo 2263  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-sbc 3126  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-uni 3980  df-br 4177  df-opab 4231  df-id 4462  df-xp 4847  df-rel 4848  df-cnv 4849  df-co 4850  df-dm 4851  df-iota 5381  df-fun 5419  df-fv 5425  df-ov 6047  df-oprab 6048  df-mpt2 6049  df-neg 9254  df-z 10243  df-fz 11004
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