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

Theorem reean 3024
Description: Rearrange restricted 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:   ,   ,   ,

Proof of Theorem reean
StepHypRef Expression
1 an4 824 . . . 4
212exbii 1668 . . 3
3 nfv 1707 . . . . 5
4 reean.1 . . . . 5
53, 4nfan 1928 . . . 4
6 nfv 1707 . . . . 5
7 reean.2 . . . . 5
86, 7nfan 1928 . . . 4
95, 8eean 1987 . . 3
102, 9bitri 249 . 2
11 r2ex 2980 . 2
12 df-rex 2813 . . 3
13 df-rex 2813 . . 3
1412, 13anbi12i 697 . 2
1510, 11, 143bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  E.wex 1612  F/wnf 1616  e.wcel 1818  E.wrex 2808
This theorem is referenced by:  reeanv  3025
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-ex 1613  df-nf 1617  df-ral 2812  df-rex 2813
  Copyright terms: Public domain W3C validator