Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eeeanv Structured version   Unicode version

Theorem eeeanv 1938
 Description: Rearrange existential quantifiers. Revised to loosen distinct variable restrictions. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.) (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 1937 . . 3
21anbi1i 677 . 2
3 df-3an 938 . . . . . 6
43exbii 1592 . . . . 5
5 19.42v 1928 . . . . 5
64, 5bitri 241 . . . 4
762exbii 1593 . . 3
8 nfv 1629 . . . . . 6
98nfex 1865 . . . . 5
10919.41 1900 . . . 4
1110exbii 1592 . . 3
12 nfv 1629 . . . . 5
1312nfex 1865 . . . 4
141319.41 1900 . . 3
157, 11, 143bitri 263 . 2
16 df-3an 938 . 2
172, 15, 163bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   w3a 936  wex 1550 This theorem is referenced by:  vtocl3  3000  spc3egv  3032  eloprabga  6152 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 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1551  df-nf 1554
 Copyright terms: Public domain W3C validator