Theorem ssv 3019

Description: Any class is a subclass of the universal class. (Contributed by NM, 31-Oct-1995.)

Assertion

Ref	Expression
ssv	|- A C_ _V

Proof of Theorem ssv

Dummy variable x is distinct from all other variables.

Step	Hyp	Ref	Expression
1		elex 2610	. 2 |- ( x e. A -> x e. _V )
2	1	ssriv 3003	1 |- A C_ _V

Syntax hints:   _Vcvv 2601   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-v 2603  df-in 2979  df-ss 2986

This theorem is referenced by:  ddifss  3202  inv1  3280  unv  3281  vss  3291  disj2  3299  pwv  3600  trv  3887  xpss  4464  djussxp  4499  dmv  4569  dmresi  4681  resid  4682  ssrnres  4783  rescnvcnv  4803  cocnvcnv1  4851  relrelss  4864  dffn2  5067  oprabss  5610  ofmres  5783  f1stres  5806  f2ndres  5807