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Theorem raaan 3727
 Description: Rearrange restricted quantifiers. (Contributed by NM, 26-Oct-2010.)
Hypotheses
Ref Expression
raaan.1
raaan.2
Assertion
Ref Expression
raaan
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem raaan
StepHypRef Expression
1 rzal 3721 . . 3
2 rzal 3721 . . 3
3 rzal 3721 . . 3
4 pm5.1 831 . . 3
51, 2, 3, 4syl12anc 1182 . 2
6 raaan.1 . . . . 5
76r19.28z 3712 . . . 4
87ralbidv 2717 . . 3
9 nfcv 2571 . . . . 5
10 raaan.2 . . . . 5
119, 10nfral 2751 . . . 4
1211r19.27z 3718 . . 3
138, 12bitrd 245 . 2
145, 13pm2.61ine 2674 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wnf 1553   wceq 1652   wne 2598  wral 2697  c0 3620 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 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-v 2950  df-dif 3315  df-nul 3621
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