ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  euxfr2dc Structured version   Unicode version

Theorem euxfr2dc 2720
Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.)
Hypotheses
Ref Expression
euxfr2dc.1  _V
euxfr2dc.2
Assertion
Ref Expression
euxfr2dc DECID
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem euxfr2dc
StepHypRef Expression
1 euxfr2dc.2 . . . . . . 7
21moani 1967 . . . . . 6
3 ancom 253 . . . . . . 7
43mobii 1934 . . . . . 6
52, 4mpbi 133 . . . . 5
65ax-gen 1335 . . . 4
7 excom 1551 . . . . . 6
87dcbii 746 . . . . 5 DECID DECID
9 2euswapdc 1988 . . . . 5 DECID
108, 9sylbi 114 . . . 4 DECID
116, 10mpi 15 . . 3 DECID
12 moeq 2710 . . . . . . 7
1312moani 1967 . . . . . 6
143mobii 1934 . . . . . 6
1513, 14mpbi 133 . . . . 5
1615ax-gen 1335 . . . 4
17 2euswapdc 1988 . . . 4 DECID
1816, 17mpi 15 . . 3 DECID
1911, 18impbid 120 . 2 DECID
20 euxfr2dc.1 . . . 4  _V
21 biidd 161 . . . 4
2220, 21ceqsexv 2587 . . 3
2322eubii 1906 . 2
2419, 23syl6bb 185 1 DECID
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  DECID wdc 741  wal 1240   wceq 1242  wex 1378   wcel 1390  weu 1897  wmo 1898   _Vcvv 2551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-dc 742  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by:  euxfrdc  2721
  Copyright terms: Public domain W3C validator