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Theorem raaan 3470
 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 raaan.1 . . . 4
2 raaan.2 . . . 4
31, 2raaanlem 3469 . . 3
43pm5.74i 179 . 2
5 ralm 3468 . 2
6 jcab 593 . . 3
7 ralm 3468 . . . 4
8 eleq1 2203 . . . . . . 7
98cbvexv 1891 . . . . . 6
109imbi1i 237 . . . . 5
11 ralm 3468 . . . . 5
1210, 11bitri 183 . . . 4
137, 12anbi12i 456 . . 3
146, 13bitri 183 . 2
154, 5, 143bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wnf 1437  wex 1469   wcel 1481  wral 2417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422 This theorem is referenced by:  raaanv  3471
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