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Theorem 0ss 3579
 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

Proof of Theorem 0ss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 noel 3554 . . 3
21pm2.21i 123 . 2
32ssriv 3277 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1710   wss 3257  c0 3550 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-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by:  ss0b  3580  0pss  3588  npss0  3589  ssdifeq0  3632  pwpw0  3855  sssn  3864  sspr  3869  sstp  3870  pwsnALT  3882  uni0  3918  int0el  3957  iotassuni  4355  0ima  5014  dmxpss  5052  dmsnopss  5067  fun0  5154  f0  5248  fvmptss  5705  fvmptss2  5725  clos10  5887  mapsspm  6021  mapsspw  6022  map0e  6023  lec0cg  6198  0lt1c  6258  frecxp  6314
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