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

Theorem rabsn 4010
 Description: Condition where a restricted class abstraction is a singleton. (Contributed by NM, 28-May-2006.)
Assertion
Ref Expression
rabsn
Distinct variable groups:   ,   ,

Proof of Theorem rabsn
StepHypRef Expression
1 eleq1 2494 . . . . 5
21pm5.32ri 642 . . . 4
32baib 911 . . 3
43abbidv 2546 . 2
5 df-rab 2723 . 2
6 df-sn 3942 . 2
74, 5, 63eqtr4g 2487 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   wcel 1872  cab 2414  crab 2718  csn 3941 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-rab 2723  df-sn 3942 This theorem is referenced by:  unisn3  4179  sylow3lem6  17227  lineunray  30863  pmapat  33240  dia0  34532  nzss  36579  lco0  39823
 Copyright terms: Public domain W3C validator