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Theorem dfco2a 5371
 Description: Generalization of dfco2 5370, where can have any value between and . (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
dfco2a
Distinct variable groups:   ,   ,   ,

Proof of Theorem dfco2a
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfco2 5370 . 2
2 vex 2960 . . . . . . . . . . . . . 14
3 vex 2960 . . . . . . . . . . . . . . 15
43eliniseg 5234 . . . . . . . . . . . . . 14
52, 4ax-mp 8 . . . . . . . . . . . . 13
63, 2brelrn 5101 . . . . . . . . . . . . 13
75, 6sylbi 189 . . . . . . . . . . . 12
8 vex 2960 . . . . . . . . . . . . . 14
92, 8elimasn 5230 . . . . . . . . . . . . 13
102, 8opeldm 5074 . . . . . . . . . . . . 13
119, 10sylbi 189 . . . . . . . . . . . 12
127, 11anim12ci 552 . . . . . . . . . . 11
1312adantl 454 . . . . . . . . . 10
1413exlimivv 1646 . . . . . . . . 9
15 elxp 4896 . . . . . . . . 9
16 elin 3531 . . . . . . . . 9
1714, 15, 163imtr4i 259 . . . . . . . 8
18 ssel 3343 . . . . . . . 8
1917, 18syl5 31 . . . . . . 7
2019pm4.71rd 618 . . . . . 6
2120exbidv 1637 . . . . 5
22 rexv 2971 . . . . 5
23 df-rex 2712 . . . . 5
2421, 22, 233bitr4g 281 . . . 4
25 eliun 4098 . . . 4
26 eliun 4098 . . . 4
2724, 25, 263bitr4g 281 . . 3
2827eqrdv 2435 . 2
291, 28syl5eq 2481 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726  wrex 2707  cvv 2957   cin 3320   wss 3321  csn 3815  cop 3818  ciun 4094   class class class wbr 4213   cxp 4877  ccnv 4878   cdm 4879   crn 4880  cima 4882   ccom 4883 This theorem is referenced by:  fparlem3  6449  fparlem4  6450 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-iun 4096  df-br 4214  df-opab 4268  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-rn 4890  df-res 4891  df-ima 4892
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