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Theorem eeeanv 1989
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:   ,   ,   ,   ,   ,   ,

Proof of Theorem eeeanv
StepHypRef Expression
1 eeanv 1988 . . 3
21anbi1i 695 . 2
3 df-3an 975 . . . . . 6
43exbii 1667 . . . . 5
5 19.42v 1775 . . . . 5
64, 5bitri 249 . . . 4
762exbii 1668 . . 3
8 nfv 1707 . . . . . 6
98nfex 1948 . . . . 5
10919.41 1971 . . . 4
1110exbii 1667 . . 3
12 nfv 1707 . . . . 5
1312nfex 1948 . . . 4
141319.41 1971 . . 3
157, 11, 143bitri 271 . 2
16 df-3an 975 . 2
172, 15, 163bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  E.wex 1612
This theorem is referenced by:  vtocl3  3163  spc3egv  3198  eloprabga  6389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-nf 1617
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