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Theorem ssv 2965
 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 2566 . 2 (𝑥𝐴𝑥 ∈ V)
21ssriv 2949 1 𝐴 ⊆ V
 Colors of variables: wff set class Syntax hints:  Vcvv 2557   ⊆ wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559  df-in 2924  df-ss 2931 This theorem is referenced by:  ddifss  3175  inv1  3253  unv  3254  vss  3264  pssv  3267  disj2  3275  pwv  3579  trv  3866  xpss  4446  djussxp  4481  dmv  4551  dmresi  4661  resid  4662  ssrnres  4763  rescnvcnv  4783  cocnvcnv1  4831  relrelss  4844  dffn2  5047  oprabss  5590  ofmres  5763  f1stres  5786  f2ndres  5787
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