Theorem ssv 3291

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 2867	. 2 ⊢ (x ∈ A → x ∈ V)
2	1	ssriv 3277	1 ⊢ A ⊆ V

Syntax hints:  Vcvv 2859   ⊆ wss 3257

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259

This theorem is referenced by:  inv1  3577  unv  3578  vss  3587  pssv  3590  disj2  3598  pwv  3886  unissint  3950  vfinnc  4471  vfinspsslem1  4550  dmv  4920  dmresi  5004  resid  5005  ssrnres  5059  dffn2  5224  f1funfun  5263  swapres  5512  pw1fnf1o  5855  fvfullfunlem3  5863  dfnnc3  5885  fundmen  6043  xpassen  6057  lecncvg  6199