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

Theorem eluniab 3592
 Description: Membership in union of a class abstraction. (Contributed by NM, 11-Aug-1994.) (Revised by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
eluniab
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem eluniab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eluni 3583 . 2
2 nfv 1421 . . . 4
3 nfsab1 2030 . . . 4
42, 3nfan 1457 . . 3
5 nfv 1421 . . 3
6 eleq2 2101 . . . 4
7 eleq1 2100 . . . . 5
8 abid 2028 . . . . 5
97, 8syl6bb 185 . . . 4
106, 9anbi12d 442 . . 3
114, 5, 10cbvex 1639 . 2
121, 11bitri 173 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wex 1381   wcel 1393  cab 2026  cuni 3580 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-uni 3581 This theorem is referenced by:  elunirab  3593  dfiun2g  3689  inuni  3909  snnex  4181  elfv  5176  unielxp  5800  tfrlem9  5935  tfr0  5937
 Copyright terms: Public domain W3C validator