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

Theorem rabss 3017
 Description: Restricted class abstraction in a subclass relationship. (Contributed by NM, 16-Aug-2006.)
Assertion
Ref Expression
rabss
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rabss
StepHypRef Expression
1 df-rab 2315 . . 3
21sseq1i 2969 . 2
3 abss 3009 . 2
4 impexp 250 . . . 4
54albii 1359 . . 3
6 df-ral 2311 . . 3
75, 6bitr4i 176 . 2
82, 3, 73bitri 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wcel 1393  cab 2026  wral 2306  crab 2310   wss 2917 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-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rab 2315  df-in 2924  df-ss 2931 This theorem is referenced by:  rabssdv  3020
 Copyright terms: Public domain W3C validator