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Theorem fzval 9732
 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 3900 . . . 4
21anbi1d 458 . . 3
32rabbidv 2647 . 2
4 breq2 3901 . . . 4
54anbi2d 457 . . 3
65rabbidv 2647 . 2
7 df-fz 9731 . 2
8 zex 9014 . . 3
98rabex 4040 . 2
103, 6, 7, 9ovmpo 5872 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1314   wcel 1463  crab 2395   class class class wbr 3897  (class class class)co 5740   cle 7765  cz 9005  cfz 9730 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-pow 4066  ax-pr 4099  ax-setind 4420  ax-cnex 7675  ax-resscn 7676 This theorem depends on definitions:  df-bi 116  df-3or 946  df-3an 947  df-tru 1317  df-fal 1320  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ne 2284  df-ral 2396  df-rex 2397  df-rab 2400  df-v 2660  df-sbc 2881  df-dif 3041  df-un 3043  df-in 3045  df-ss 3052  df-pw 3480  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-opab 3958  df-id 4183  df-xp 4513  df-rel 4514  df-cnv 4515  df-co 4516  df-dm 4517  df-iota 5056  df-fun 5093  df-fv 5099  df-ov 5743  df-oprab 5744  df-mpo 5745  df-neg 7900  df-z 9006  df-fz 9731 This theorem is referenced by:  fzval2  9733  elfz1  9735  fznlem  9761
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