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Theorem sstp 3965
 Description: The subsets of a triple. (Contributed by Mario Carneiro, 2-Jul-2016.)
Assertion
Ref Expression
sstp

Proof of Theorem sstp
StepHypRef Expression
1 df-tp 3824 . . 3
21sseq2i 3375 . 2
3 0ss 3658 . . 3
43biantrur 494 . 2
5 ssunsn2 3960 . . 3
63biantrur 494 . . . . 5
7 sspr 3964 . . . . 5
86, 7bitr3i 244 . . . 4
9 uncom 3493 . . . . . . . 8
10 un0 3654 . . . . . . . 8
119, 10eqtri 2458 . . . . . . 7
1211sseq1i 3374 . . . . . 6
13 uncom 3493 . . . . . . 7
1413sseq2i 3375 . . . . . 6
1512, 14anbi12i 680 . . . . 5
16 ssunpr 3963 . . . . 5
17 uncom 3493 . . . . . . . . 9
18 df-pr 3823 . . . . . . . . 9
1917, 18eqtr4i 2461 . . . . . . . 8
2019eqeq2i 2448 . . . . . . 7
2120orbi2i 507 . . . . . 6
22 uncom 3493 . . . . . . . . 9
23 df-pr 3823 . . . . . . . . 9
2422, 23eqtr4i 2461 . . . . . . . 8
2524eqeq2i 2448 . . . . . . 7
261, 13eqtr2i 2459 . . . . . . . 8
2726eqeq2i 2448 . . . . . . 7
2825, 27orbi12i 509 . . . . . 6
2921, 28orbi12i 509 . . . . 5
3015, 16, 293bitri 264 . . . 4
318, 30orbi12i 509 . . 3
325, 31bitri 242 . 2
332, 4, 323bitri 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  ctp 3818 This theorem is referenced by:  pwtp  4014 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  df-tp 3824
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