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Theorem imasng 4617
Description: The image of a singleton. (Contributed by NM, 8-May-2005.)
Assertion
Ref Expression
imasng  R " { }  {  |  R }
Distinct variable groups:   ,   , R
Allowed substitution hint:   ()

Proof of Theorem imasng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2543 . 2  _V
2 dfima2 4597 . . 3  R
" { }  {  |  { } R }
3 breq1 3741 . . . . 5  R  R
43rexsng 3386 . . . 4  _V  { } R  R
54abbidv 2137 . . 3  _V  {  |  { } R }  {  |  R }
62, 5syl5eq 2066 . 2  _V  R " { }  {  |  R }
71, 6syl 14 1  R " { }  {  |  R }
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1228   wcel 1374   {cab 2008  wrex 2285   _Vcvv 2535   {csn 3350   class class class wbr 3738   "cima 4275
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-sep 3849  ax-pow 3901  ax-pr 3918
This theorem depends on definitions:  df-bi 110  df-3an 875  df-tru 1231  df-nf 1330  df-sb 1628  df-eu 1885  df-mo 1886  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289  df-rex 2290  df-v 2537  df-sbc 2742  df-un 2899  df-in 2901  df-ss 2908  df-pw 3336  df-sn 3356  df-pr 3357  df-op 3359  df-br 3739  df-opab 3793  df-xp 4278  df-cnv 4280  df-dm 4282  df-rn 4283  df-res 4284  df-ima 4285
This theorem is referenced by:  elreimasng  4618  elimasn  4619  args  4621  fnsnfv  5157  funfvdm2  5162  dfec2  6020
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