ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  eusv2nf Unicode version

Theorem eusv2nf 4154
Description: Two ways to express single-valuedness of a class expression . (Contributed by Mario Carneiro, 18-Nov-2016.)
Hypothesis
Ref Expression
eusv2.1  _V
Assertion
Ref Expression
eusv2nf  F/_
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eusv2nf
StepHypRef Expression
1 nfeu1 1908 . . . 4  F/
2 nfe1 1382 . . . . . . 7  F/
32nfeu 1916 . . . . . 6  F/
4 eusv2.1 . . . . . . . . 9  _V
54isseti 2557 . . . . . . . 8
6 19.8a 1479 . . . . . . . . 9
76ancri 307 . . . . . . . 8
85, 7eximii 1490 . . . . . . 7
9 eupick 1976 . . . . . . 7
108, 9mpan2 401 . . . . . 6
113, 10alrimi 1412 . . . . 5
12 nf3 1556 . . . . 5  F/
1311, 12sylibr 137 . . . 4  F/
141, 13alrimi 1412 . . 3  F/
15 dfnfc2 3589 . . . 4  _V  F/_  F/
1615, 4mpg 1337 . . 3  F/_  F/
1714, 16sylibr 137 . 2  F/_
18 eusvnfb 4152 . . . 4  F/_  _V
194, 18mpbiran2 847 . . 3  F/_
20 eusv2i 4153 . . 3
2119, 20sylbir 125 . 2  F/_
2217, 21impbii 117 1  F/_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242   F/wnf 1346  wex 1378   wcel 1390  weu 1897   F/_wnfc 2162   _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-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-bndl 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-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-sbc 2759  df-csb 2847  df-un 2916  df-sn 3373  df-pr 3374  df-uni 3572
This theorem is referenced by:  eusv2  4155
  Copyright terms: Public domain W3C validator