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

Theorem elrab 2692
Description: Membership in a restricted class abstraction, using implicit substitution. (Contributed by NM, 21-May-1999.)
Hypothesis
Ref Expression
elrab.1
Assertion
Ref Expression
elrab  {  |  }
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem elrab
StepHypRef Expression
1 nfcv 2175 . 2  F/_
2 nfcv 2175 . 2  F/_
3 nfv 1418 . 2  F/
4 elrab.1 . 2
51, 2, 3, 4elrabf 2690 1  {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   wcel 1390   {crab 2304
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-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309  df-v 2553
This theorem is referenced by:  elrab3  2693  elrab2  2694  ralrab  2696  rexrab  2698  rabsnt  3436  unimax  3605  ssintub  3624  intminss  3631  rabxfrd  4167  onsucelsucexmidlem1  4213  sefvex  5139  ssimaex  5177  acexmidlem2  5452  ssfiexmid  6254  caucvgprlemladdfu  6648  caucvgprlemladdrl  6649  nnind  7711  peano2uz2  8121  peano5uzti  8122  dfuzi  8124  uzind  8125  uzind3  8127  eluz1  8253  uzind4  8307  eqreznegel  8325  elixx1  8536  elioo2  8560  elfz1  8649  expcl2lemap  8921  expclzaplem  8933  expclzap  8934  expap0i  8941  expge0  8945  expge1  8946
  Copyright terms: Public domain W3C validator