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Theorem raaan 3937
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 3931 . . 3
2 rzal 3931 . . 3
3 rzal 3931 . . 3
4 pm5.1 857 . . 3
51, 2, 3, 4syl12anc 1226 . 2
6 raaan.1 . . . . 5
76r19.28z 3921 . . . 4
87ralbidv 2896 . . 3
9 nfcv 2619 . . . . 5
10 raaan.2 . . . . 5
119, 10nfral 2843 . . . 4
1211r19.27z 3928 . . 3
138, 12bitrd 253 . 2
145, 13pm2.61ine 2770 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  =/=wne 2652  A.wral 2807   c0 3784
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-nul 3785
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