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Theorem npss0 3266
 Description: No set is a proper subset of the empty set. (Contributed by NM, 17-Jun-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
npss0

Proof of Theorem npss0
StepHypRef Expression
1 0ss 3255 . . . 4
21a1i 9 . . 3
3 imanim 785 . . 3
42, 3ax-mp 7 . 2
5 dfpss3 3030 . 2
64, 5mtbir 596 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wss 2917   wpss 2918  c0 3224 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-v 2559  df-dif 2920  df-in 2924  df-ss 2931  df-pss 2933  df-nul 3225 This theorem is referenced by: (None)
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