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Theorem sspr 3964
 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 3493 . . . . 5
2 un0 3654 . . . . 5
31, 2eqtri 2458 . . . 4
43sseq2i 3375 . . 3
5 0ss 3658 . . . 4
65biantrur 494 . . 3
74, 6bitr3i 244 . 2
8 ssunpr 3963 . 2
9 uncom 3493 . . . . . 6
10 un0 3654 . . . . . 6
119, 10eqtri 2458 . . . . 5
1211eqeq2i 2448 . . . 4
1312orbi2i 507 . . 3
14 uncom 3493 . . . . . 6
15 un0 3654 . . . . . 6
1614, 15eqtri 2458 . . . . 5
1716eqeq2i 2448 . . . 4
183eqeq2i 2448 . . . 4
1917, 18orbi12i 509 . . 3
2013, 19orbi12i 509 . 2
217, 8, 203bitri 264 1
 Colors of variables: wff set class Syntax hints:   wb 178   wo 359   wa 360   wceq 1653   cun 3320   wss 3322  c0 3630  csn 3816  cpr 3817 This theorem is referenced by:  sstp  3965  pwpr  4013  indistopon  17070 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-sn 3822  df-pr 3823
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