Theorem ssv 3046

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.

Step	Hyp	Ref	Expression
1		elex 2630	. 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ V)
2	1	ssriv 3029	1 ⊢ 𝐴 ⊆ V

Syntax hints:  Vcvv 2619   ⊆ wss 2999

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 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-v 2621  df-in 3005  df-ss 3012

This theorem is referenced by:  ddifss  3237  inv1  3319  unv  3320  vss  3330  disj2  3338  pwv  3652  trv  3948  xpss  4546  djussxp  4581  dmv  4652  dmresi  4767  resid  4768  ssrnres  4873  rescnvcnv  4893  cocnvcnv1  4941  relrelss  4957  dffn2  5163  oprabss  5734  ofmres  5907  f1stres  5930  f2ndres  5931  fiintim  6637  djuf1olemr  6744  dju1p1e2  6821  seq3val  9870  seq3-1  9873  seqf  9876  seq3p1  9880  seq3feq  9893  seq3shft2  9895  iseqseq3  9898  setscom  11529