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Theorem ssv 2993
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 2583 . 2 (𝑥𝐴𝑥 ∈ V)
21ssriv 2977 1 𝐴 ⊆ V
Colors of variables: wff set class
Syntax hints:  Vcvv 2574  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576  df-in 2952  df-ss 2959
This theorem is referenced by:  ddifss  3203  inv1  3281  unv  3282  vss  3292  pssv  3295  disj2  3303  pwv  3607  trv  3894  xpss  4474  djussxp  4509  dmv  4579  dmresi  4689  resid  4690  ssrnres  4791  rescnvcnv  4811  cocnvcnv1  4859  relrelss  4872  dffn2  5075  oprabss  5618  ofmres  5791  f1stres  5814  f2ndres  5815
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