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Theorem raaan 3657
 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 3651 . . 3
2 rzal 3651 . . 3
3 rzal 3651 . . 3
4 pm5.1 830 . . 3
51, 2, 3, 4syl12anc 1180 . 2
6 raaan.1 . . . . 5
76r19.28z 3642 . . . 4
87ralbidv 2634 . . 3
9 nfcv 2489 . . . . 5
10 raaan.2 . . . . 5
119, 10nfral 2667 . . . 4
1211r19.27z 3648 . . 3
138, 12bitrd 244 . 2
145, 13pm2.61ine 2592 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wnf 1544   wceq 1642   wne 2516  wral 2614  c0 3550 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-nul 3551 This theorem is referenced by: (None)
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