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Theorem ssv 3150
Description: Any class is a subclass of the universal class. (Contributed by NM, 31-Oct-1995.)
Assertion
Ref Expression
ssv 𝐴 ⊆ V

Proof of Theorem ssv
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 elex 2723 . 2 (𝑥𝐴𝑥 ∈ V)
21ssriv 3132 1 𝐴 ⊆ V
Colors of variables: wff set class
Syntax hints:  Vcvv 2712  wss 3102
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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-v 2714  df-in 3108  df-ss 3115
This theorem is referenced by:  ddifss  3346  inv1  3431  unv  3432  vss  3442  disj2  3450  pwv  3773  trv  4077  xpss  4697  djussxp  4734  dmv  4805  dmresi  4924  resid  4925  ssrnres  5031  rescnvcnv  5051  cocnvcnv1  5099  relrelss  5115  dffn2  5324  oprabss  5910  ofmres  6087  f1stres  6110  f2ndres  6111  fiintim  6876  djuf1olemr  7001  endjusym  7043  dju1p1e2  7135  suplocexprlemell  7636  seq3val  10367  seqvalcd  10368  seq3-1  10369  seqf  10370  seq3p1  10371  seqf2  10373  seq1cd  10374  seqp1cd  10375  setscom  12326  upxp  12768  uptx  12770  cnmptid  12777  cnmpt1st  12784  cnmpt2nd  12785
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