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Theorem eeeanv 2079
 Description: Rearrange existential quantifiers. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.) Reduce distinct variable restrictions. (Revised by Wolf Lammen, 20-Jan-2018.)
Assertion
Ref Expression
eeeanv
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem eeeanv
StepHypRef Expression
1 eeanv 2078 . . 3
21anbi1i 701 . 2
3 df-3an 987 . . . . . 6
43exbii 1718 . . . . 5
5 19.42v 1834 . . . . 5
64, 5bitri 253 . . . 4
762exbii 1719 . . 3
8 nfv 1761 . . . . . 6
98nfex 2031 . . . . 5
10919.41 2051 . . . 4
1110exbii 1718 . . 3
12 nfv 1761 . . . . 5
1312nfex 2031 . . . 4
141319.41 2051 . . 3
157, 11, 143bitri 275 . 2
16 df-3an 987 . 2
172, 15, 163bitr4i 281 1
 Colors of variables: wff setvar class Syntax hints:   wb 188   wa 371   w3a 985  wex 1663 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-an 373  df-3an 987  df-ex 1664  df-nf 1668 This theorem is referenced by:  vtocl3  3103  spc3egv  3138  eloprabga  6383
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