Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ss2rab Structured version   Unicode version

Theorem ss2rab 3421
 Description: Restricted abstraction classes in a subclass relationship. (Contributed by NM, 30-May-1999.)
Assertion
Ref Expression
ss2rab

Proof of Theorem ss2rab
StepHypRef Expression
1 df-rab 2716 . . 3
2 df-rab 2716 . . 3
31, 2sseq12i 3376 . 2
4 ss2ab 3413 . 2
5 df-ral 2712 . . 3
6 imdistan 672 . . . 4
76albii 1576 . . 3
85, 7bitr2i 243 . 2
93, 4, 83bitri 264 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wcel 1726  cab 2424  wral 2707  crab 2711   wss 3322 This theorem is referenced by:  ss2rabdv  3426  ss2rabi  3427  scottex  7811  ondomon  8440  eltsms  18164  xrlimcnp  20809  occon  22791  spanss  22852  chpssati  23868  rmxyelqirr  26975  itgoss  27347  lpssat  29873  lssatle  29875  lssat  29876  atlatle  30180  pmaple  30620  diaord  31907  mapdordlem2  32497 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rab 2716  df-in 3329  df-ss 3336
 Copyright terms: Public domain W3C validator