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Theorem reean 2478
 Description: Rearrange existential quantifiers. (Contributed by NM, 27-Oct-2010.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Hypotheses
Ref Expression
reean.1
reean.2
Assertion
Ref Expression
reean
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   (,)   ()   ()

Proof of Theorem reean
StepHypRef Expression
1 an4 520 . . . 4
212exbii 1497 . . 3
3 nfv 1421 . . . . 5
4 reean.1 . . . . 5
53, 4nfan 1457 . . . 4
6 nfv 1421 . . . . 5
7 reean.2 . . . . 5
86, 7nfan 1457 . . . 4
95, 8eean 1806 . . 3
102, 9bitri 173 . 2
11 r2ex 2344 . 2
12 df-rex 2312 . . 3
13 df-rex 2312 . . 3
1412, 13anbi12i 433 . 2
1510, 11, 143bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wnf 1349  wex 1381   wcel 1393  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312 This theorem is referenced by:  reeanv  2479
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