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Theorem disjpss 3601
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 3290 . . . . . . . 8
21biantru 491 . . . . . . 7
3 ssin 3477 . . . . . . 7
42, 3bitri 240 . . . . . 6
5 sseq2 3293 . . . . . 6
64, 5syl5bb 248 . . . . 5
7 ss0 3581 . . . . 5
86, 7syl6bi 219 . . . 4
98necon3ad 2552 . . 3
109imp 418 . 2
11 nsspssun 3488 . . 3
12 uncom 3408 . . . 4
1312psseq2i 3359 . . 3
1411, 13bitri 240 . 2
1510, 14sylib 188 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wa 358   wceq 1642   wne 2516   cun 3207   cin 3208   wss 3257   wpss 3258  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-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-pss 3261  df-nul 3551
This theorem is referenced by: (None)
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