ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  class2seteq Structured version   Unicode version

Theorem class2seteq 3907
Description: Equality theorem for classes and sets . (Contributed by NM, 13-Dec-2005.) (Proof shortened by Raph Levien, 30-Jun-2006.)
Assertion
Ref Expression
class2seteq  V  {  |  _V }
Distinct variable group:   ,
Allowed substitution hint:    V()

Proof of Theorem class2seteq
StepHypRef Expression
1 elex 2560 . 2  V  _V
2 ax-1 5 . . . . 5  _V  _V
32ralrimiv 2385 . . . 4  _V  _V
4 rabid2 2480 . . . 4  {  |  _V }  _V
53, 4sylibr 137 . . 3  _V  {  |  _V }
65eqcomd 2042 . 2  _V  {  |  _V }
71, 6syl 14 1  V  {  |  _V }
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390  wral 2300   {crab 2304   _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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  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-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-rab 2309  df-v 2553
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator