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Theorem fzval 10662
 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
StepHypRef Expression
1 breq1 3923 . . . 4
21anbi1d 688 . . 3
32rabbidv 2719 . 2
4 breq2 3924 . . . 4
54anbi2d 687 . . 3
65rabbidv 2719 . 2
7 df-fz 10661 . 2
8 zex 9912 . . 3
98rabex 4061 . 2
103, 6, 7, 9ovmpt2 5835 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360   wceq 1619   wcel 1621  crab 2512   class class class wbr 3920  (class class class)co 5710   cle 8748  cz 9903  cfz 10660 This theorem is referenced by:  fzval2  10663  elfz1  10665 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-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-cnex 8673  ax-resscn 8674 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-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-br 3921  df-opab 3975  df-id 4202  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-ov 5713  df-oprab 5714  df-mpt2 5715  df-neg 8920  df-z 9904  df-fz 10661
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