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Theorem pssdifn0 3888
Description: A proper subclass has a nonempty difference. (Contributed by NM, 3-May-1994.)
Assertion
Ref Expression
pssdifn0

Proof of Theorem pssdifn0
StepHypRef Expression
1 ssdif0 3885 . . . 4
2 eqss 3518 . . . . 5
32simplbi2 625 . . . 4
41, 3syl5bir 218 . . 3
54necon3d 2681 . 2
65imp 429 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  =/=wne 2652  \cdif 3472  C_wss 3475   c0 3784
This theorem is referenced by:  pssdif  3889  tz7.7  4909  domdifsn  7620  inf3lem3  8068  isf32lem6  8759  fclscf  20526  flimfnfcls  20529  lebnumlem1  21461  lebnumlem2  21462  lebnumlem3  21463  ig1peu  22572  ig1pdvds  22577  divrngidl  30425
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-or 370  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-nul 3785
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