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

Theorem abss 3255
 Description: Class abstraction in a subclass relationship. (Contributed by NM, 16-Aug-2006.)
Assertion
Ref Expression
abss
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem abss
StepHypRef Expression
1 abid2 2413 . . 3
21sseq2i 3216 . 2
3 ss2ab 3254 . 2
42, 3bitr3i 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530   wcel 1696  cab 2282   wss 3165 This theorem is referenced by:  abssdv  3260  rabss  3263  uniiunlem  3273  iunss  3959  moabex  4248  reliun  4822  axdc2lem  8090  mptelee  24595  qusp  25645 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-in 3172  df-ss 3179
 Copyright terms: Public domain W3C validator