Theorem ssv 3292

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 2868	. 2 ⊢ (x ∈ A → x ∈ V)
2	1	ssriv 3278	1 ⊢ A ⊆ V

Syntax hints:  Vcvv 2860   ⊆ wss 3258

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 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-ss 3260

This theorem is referenced by:  inv1  3578  unv  3579  vss  3588  pssv  3591  disj2  3599  pwv  3887  unissint  3951  vfinnc  4472  vfinspsslem1  4551  dmv  4921  dmresi  5005  resid  5006  ssrnres  5060  dffn2  5225  f1funfun  5264  swapres  5513  pw1fnf1o  5856  fvfullfunlem3  5864  dfnnc3  5886  fundmen  6044  xpassen  6058  lecncvg  6200