New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  abssi Unicode version

Theorem abssi 3341
 Description: Inference of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006.)
Hypothesis
Ref Expression
abssi.1
Assertion
Ref Expression
abssi
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem abssi
StepHypRef Expression
1 abssi.1 . . 3
21ss2abi 3338 . 2
3 abid2 2470 . 2
42, 3sseqtri 3303 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1710  cab 2339   wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  ssab2  3350  abf  3584  intab  3956  opkabssvvk  4208  fvclss  5462  mapsspw  6022  spacssnc  6284
 Copyright terms: Public domain W3C validator