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Theorem disjpss 3877
Description: A class is a proper subset of its union with a disjoint nonempty class. (Contributed by NM, 15-Sep-2004.)
Assertion
Ref Expression
disjpss

Proof of Theorem disjpss
StepHypRef Expression
1 ssid 3522 . . . . . . . 8
21biantru 505 . . . . . . 7
3 ssin 3719 . . . . . . 7
42, 3bitri 249 . . . . . 6
5 sseq2 3525 . . . . . 6
64, 5syl5bb 257 . . . . 5
7 ss0 3816 . . . . 5
86, 7syl6bi 228 . . . 4
98necon3ad 2667 . . 3
109imp 429 . 2
11 nsspssun 3730 . . 3
12 uncom 3647 . . . 4
1312psseq2i 3593 . . 3
1411, 13bitri 249 . 2
1510, 14sylib 196 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  =/=wne 2652  u.cun 3473  i^icin 3474  C_wss 3475  C.wpss 3476   c0 3784
This theorem is referenced by:  isfin1-3  8787
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-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785
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