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Theorem eeeanv 1914
Description: Rearrange existential quantifiers. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
eeeanv
Distinct variable groups:   ,   ,   ,,   ,,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem eeeanv
StepHypRef Expression
1 df-3an 936 . . 3
213exbii 1584 . 2
3 eeanv 1913 . . 3
43exbii 1582 . 2
5 eeanv 1913 . . . 4
65anbi1i 676 . . 3
7 19.41v 1901 . . 3
8 df-3an 936 . . 3
96, 7, 83bitr4i 268 . 2
102, 4, 93bitri 262 1
Colors of variables: wff setvar class
Syntax hints:   wb 176   wa 358   w3a 934  wex 1541
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
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-ex 1542  df-nf 1545
This theorem is referenced by:  vtocl3  2911  spc3egv  2943  eloprabga  5578  mucass  6135  taddc  6229  letc  6231
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