Theorem ssv 3114

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 2692	. 2 |- ( x e. A -> x e. _V )
2	1	ssriv 3096	1 |- A C_ _V

Syntax hints:   _Vcvv 2681   C_ wss 3066

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683  df-in 3072  df-ss 3079

This theorem is referenced by:  ddifss  3309  inv1  3394  unv  3395  vss  3405  disj2  3413  pwv  3730  trv  4033  xpss  4642  djussxp  4679  dmv  4750  dmresi  4869  resid  4870  ssrnres  4976  rescnvcnv  4996  cocnvcnv1  5044  relrelss  5060  dffn2  5269  oprabss  5850  ofmres  6027  f1stres  6050  f2ndres  6051  fiintim  6810  djuf1olemr  6932  endjusym  6974  dju1p1e2  7046  suplocexprlemell  7514  seq3val  10224  seqvalcd  10225  seq3-1  10226  seqf  10227  seq3p1  10228  seqf2  10230  seq1cd  10231  seqp1cd  10232  setscom  11988  upxp  12430  uptx  12432  cnmptid  12439  cnmpt1st  12446  cnmpt2nd  12447