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Theorem reean 2777
 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 797 . . . 4
212exbii 1583 . . 3
3 nfv 1619 . . . . 5
4 reean.1 . . . . 5
53, 4nfan 1824 . . . 4
6 nfv 1619 . . . . 5
7 reean.2 . . . . 5
86, 7nfan 1824 . . . 4
95, 8eean 1912 . . 3
102, 9bitri 240 . 2
11 r2ex 2652 . 2
12 df-rex 2620 . . 3
13 df-rex 2620 . . 3
1412, 13anbi12i 678 . 2
1510, 11, 143bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541  wnf 1544   wcel 1710  wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620 This theorem is referenced by:  reeanv  2778
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