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Theorem elo1 13349
 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 5208 . . . . 5
21ineq1d 3698 . . . 4
3 fveq1 5870 . . . . . 6
43fveq2d 5875 . . . . 5
54breq1d 4462 . . . 4
62, 5raleqbidv 3068 . . 3
762rexbidv 2975 . 2
8 df-o1 13313 . 2
97, 8elrab2 3259 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808  i^icin 3474   class class class wbr 4452  domcdm 5004  `cfv 5593  (class class class)co 6296   cpm 7440   cc 9511   cr 9512   cpnf 9646   cle 9650   cico 11560   cabs 13067   co1 13309 This theorem is referenced by:  elo12  13350  o1f  13352  o1dm  13353 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-dm 5014  df-iota 5556  df-fv 5601  df-o1 13313
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