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Theorem elo1 12320
 Description: Elementhood in the set of eventually bounded functions. (Contributed by Mario Carneiro, 15-Sep-2014.)
Assertion
Ref Expression
elo1
Distinct variable group:   ,,,

Proof of Theorem elo1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dmeq 5070 . . . . 5
21ineq1d 3541 . . . 4
3 fveq1 5727 . . . . . 6
43fveq2d 5732 . . . . 5
54breq1d 4222 . . . 4
62, 5raleqbidv 2916 . . 3
762rexbidv 2748 . 2
8 df-o1 12284 . 2
97, 8elrab2 3094 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  wral 2705  wrex 2706   cin 3319   class class class wbr 4212   cdm 4878  cfv 5454  (class class class)co 6081   cpm 7019  cc 8988  cr 8989   cpnf 9117   cle 9121  cico 10918  cabs 12039  co1 12280 This theorem is referenced by:  elo12  12321  o1f  12323  o1dm  12324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-dm 4888  df-iota 5418  df-fv 5462  df-o1 12284
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