Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  rabss2 Unicode version

Theorem rabss2 3023
 Description: Subclass law for restricted abstraction. (Contributed by NM, 18-Dec-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
rabss2
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rabss2
StepHypRef Expression
1 pm3.45 529 . . . 4
21alimi 1344 . . 3
3 dfss2 2934 . . 3
4 ss2ab 3008 . . 3
52, 3, 43imtr4i 190 . 2
6 df-rab 2315 . 2
7 df-rab 2315 . 2
85, 6, 73sstr4g 2986 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241   wcel 1393  cab 2026  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-rab 2315  df-in 2924  df-ss 2931 This theorem is referenced by:  sess2  4075
 Copyright terms: Public domain W3C validator