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Theorem 0ss 3289
Description: The null set is a subset of any class. Part of Exercise 1 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
0ss  |-  (/)  C_  A

Proof of Theorem 0ss
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 noel 3262 . . 3  |-  -.  x  e.  (/)
21pm2.21i 608 . 2  |-  ( x  e.  (/)  ->  x  e.  A )
32ssriv 3004 1  |-  (/)  C_  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1434    C_ wss 2974   (/)c0 3258
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-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976  df-in 2980  df-ss 2987  df-nul 3259
This theorem is referenced by:  ss0b  3290  ssdifeq0  3332  sssnr  3553  ssprr  3556  uni0  3636  int0el  3674  0disj  3790  disjx0  3792  tr0  3894  0elpw  3946  fr0  4114  elnn  4354  rel0  4490  0ima  4715  fun0  4988  f0  5111  oaword1  6115  bdeq0  10816  bj-omtrans  10909
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