Theorem ssv 3020

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 2611	. 2 |- ( x e. A -> x e. _V )
2	1	ssriv 3004	1 |- A C_ _V

Syntax hints:   _Vcvv 2602   C_ wss 2974

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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-v 2604  df-in 2980  df-ss 2987

This theorem is referenced by:  ddifss  3209  inv1  3287  unv  3288  vss  3298  disj2  3306  pwv  3608  trv  3895  xpss  4474  djussxp  4509  dmv  4579  dmresi  4691  resid  4692  ssrnres  4793  rescnvcnv  4813  cocnvcnv1  4861  relrelss  4874  dffn2  5078  oprabss  5621  ofmres  5794  f1stres  5817  f2ndres  5818