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Theorem sspr 4193
 Description: The subsets of a pair. (Contributed by NM, 16-Mar-2006.) (Proof shortened by Mario Carneiro, 2-Jul-2016.)
Assertion
Ref Expression
sspr

Proof of Theorem sspr
StepHypRef Expression
1 uncom 3647 . . . . 5
2 un0 3810 . . . . 5
31, 2eqtri 2486 . . . 4
43sseq2i 3528 . . 3
5 0ss 3814 . . . 4
65biantrur 506 . . 3
74, 6bitr3i 251 . 2
8 ssunpr 4192 . 2
9 uncom 3647 . . . . . 6
10 un0 3810 . . . . . 6
119, 10eqtri 2486 . . . . 5
1211eqeq2i 2475 . . . 4
1312orbi2i 519 . . 3
14 uncom 3647 . . . . . 6
15 un0 3810 . . . . . 6
1614, 15eqtri 2486 . . . . 5
1716eqeq2i 2475 . . . 4
183eqeq2i 2475 . . . 4
1917, 18orbi12i 521 . . 3
2013, 19orbi12i 521 . 2
217, 8, 203bitri 271 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  u.cun 3473  C_wss 3475   c0 3784  {csn 4029  {cpr 4031 This theorem is referenced by:  sstp  4194  pwpr  4245  indistopon  19502 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-3an 975  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-ral 2812  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032
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