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

Theorem sikeq 4241
 Description: Equality theorem for Kuratowski singleton image. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
sikeq SIk SIk

Proof of Theorem sikeq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq2 2414 . . . . . . 7
213anbi3d 1258 . . . . . 6
322exbidv 1628 . . . . 5
43anbi2d 684 . . . 4
542exbidv 1628 . . 3
65abbidv 2467 . 2
7 df-sik 4192 . 2 SIk
8 df-sik 4192 . 2 SIk
96, 7, 83eqtr4g 2410 1 SIk SIk
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   w3a 934  wex 1541   wceq 1642   wcel 1710  cab 2339  csn 3737  copk 4057   SIk csik 4181 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sik 4192 This theorem is referenced by:  sikeqi  4242  sikeqd  4243  imagekeq  4244  sikexg  4296
 Copyright terms: Public domain W3C validator