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Theorem raaan 3901
Description: Rearrange restricted quantifiers. (Contributed by NM, 26-Oct-2010.)
Hypotheses
Ref Expression
raaan.1
raaan.2
Assertion
Ref Expression
raaan
Distinct variable group:   , ,

Proof of Theorem raaan
StepHypRef Expression
1 rzal 3895 . . 3
2 rzal 3895 . . 3
3 rzal 3895 . . 3
4 pm5.1 853 . . 3
51, 2, 3, 4syl12anc 1217 . 2
6 raaan.1 . . . . 5
76r19.28z 3886 . . . 4
87ralbidv 2847 . . 3
9 nfcv 2616 . . . . 5
10 raaan.2 . . . . 5
119, 10nfral 2889 . . . 4
1211r19.27z 3892 . . 3
138, 12bitrd 253 . 2
145, 13pm2.61ine 2766 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  =wceq 1370  F/wnf 1590  =/=wne 2648  A.wral 2800   c0 3751
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-v 3083  df-dif 3445  df-nul 3752
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