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Theorem reusv2lem5 4657
Description: Lemma for reusv2 4658. (Contributed by NM, 4-Jan-2013.) (Proof shortened by Mario Carneiro, 19-Nov-2016.)
Assertion
Ref Expression
reusv2lem5
Distinct variable groups:   , ,   , ,   ,

Proof of Theorem reusv2lem5
StepHypRef Expression
1 tru 1399 . . . . . . . . 9
2 biimt 335 . . . . . . . . 9
31, 2mpan2 671 . . . . . . . 8
4 ibar 504 . . . . . . . 8
53, 4bitr3d 255 . . . . . . 7
6 eleq1 2529 . . . . . . . 8
76pm5.32ri 638 . . . . . . 7
85, 7syl6bbr 263 . . . . . 6
98ralimi 2850 . . . . 5
10 ralbi 2988 . . . . 5
119, 10syl 16 . . . 4
1211eubidv 2304 . . 3
13 r19.28zv 3924 . . . 4
1413eubidv 2304 . . 3
1512, 14sylan9bb 699 . 2
161biantrur 506 . . . . 5
1716rexbii 2959 . . . 4
1817reubii 3044 . . 3
19 reusv2lem4 4656 . . 3
2018, 19bitri 249 . 2
21 df-reu 2814 . 2
2215, 20, 213bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395   wtru 1396  e.wcel 1818  E!weu 2282  =/=wne 2652  A.wral 2807  E.wrex 2808  E!wreu 2809   c0 3784
This theorem is referenced by:  reusv2  4658
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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581  ax-pow 4630
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-nul 3785
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