Theorem ssid 3018

Description: Any class is a subclass of itself. Exercise 10 of [TakeutiZaring] p. 18. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
ssid	|- A C_ A

Proof of Theorem ssid

Dummy variable x is distinct from all other variables.

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( x e. A -> x e. A )
2	1	ssriv 3003	1 |- A C_ A

Syntax hints:   e. wcel 1433   C_ wss 2973

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-in 2979  df-ss 2986

This theorem is referenced by:  eqimssi  3053  eqimss2i  3054  inv1  3280  difid  3312  undifabs  3320  pwidg  3395  elssuni  3629  unimax  3635  intmin  3656  rintm  3765  iunpw  4229  sucprcreg  4292  tfisi  4328  peano5  4339  xpss1  4466  xpss2  4467  residm  4660  resdm  4667  resmpt3  4677  ssrnres  4783  dffn3  5073  fimacnv  5317  tfrlem1  5946  rdgss  5993  findcard2d  6375  findcard2sd  6376  1idprl  6780  1idpru  6781  ltexprlemm  6790  elq  8707  expcl  9494  iserclim0  10144