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Theorem 0pss 3864
Description: The null set is a proper subset of any nonempty set. (Contributed by NM, 27-Feb-1996.)
Assertion
Ref Expression
0pss

Proof of Theorem 0pss
StepHypRef Expression
1 0ss 3814 . . 3
2 df-pss 3491 . . 3
31, 2mpbiran 918 . 2
4 necom 2726 . 2
53, 4bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =/=wne 2652  C_wss 3475  C.wpss 3476   c0 3784
This theorem is referenced by:  php  7721  zornn0g  8906  prn0  9388  genpn0  9402  nqpr  9413  ltexprlem5  9439  reclem2pr  9447  suplem1pr  9451  alexsubALTlem4  20550  bj-2upln0  34581  bj-2upln1upl  34582  0pssin  37794
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785
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