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Theorem reean 2874
 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 798 . . . 4
212exbii 1593 . . 3
3 nfv 1629 . . . . 5
4 reean.1 . . . . 5
53, 4nfan 1846 . . . 4
6 nfv 1629 . . . . 5
7 reean.2 . . . . 5
86, 7nfan 1846 . . . 4
95, 8eean 1936 . . 3
102, 9bitri 241 . 2
11 r2ex 2743 . 2
12 df-rex 2711 . . 3
13 df-rex 2711 . . 3
1412, 13anbi12i 679 . 2
1510, 11, 143bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550  wnf 1553   wcel 1725  wrex 2706 This theorem is referenced by:  reeanv  2875 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 2417 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-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711
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