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Theorem sorpssi 6530
 Description: Property of a chain of sets. (Contributed by Stefan O'Rear, 2-Nov-2014.)
Assertion
Ref Expression
sorpssi []

Proof of Theorem sorpssi
StepHypRef Expression
1 solin 4528 . . 3 [] [] []
2 elex 2966 . . . . . 6
32ad2antll 711 . . . . 5 []
4 brrpssg 6526 . . . . 5 []
53, 4syl 16 . . . 4 [] []
6 biidd 230 . . . 4 []
7 elex 2966 . . . . . 6
87ad2antrl 710 . . . . 5 []
9 brrpssg 6526 . . . . 5 []
108, 9syl 16 . . . 4 [] []
115, 6, 103orbi123d 1254 . . 3 [] [] []
121, 11mpbid 203 . 2 []
13 sspsstri 3451 . 2
1412, 13sylibr 205 1 []
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wo 359   wa 360   w3o 936   wceq 1653   wcel 1726  cvv 2958   wss 3322   wpss 3323   class class class wbr 4214   wor 4504   [] crpss 6523 This theorem is referenced by:  sorpssun  6531  sorpssin  6532  sorpssuni  6533  sorpssint  6534  sorpsscmpl  6535  enfin2i  8203  fin1a2lem9  8290  fin1a2lem10  8291  fin1a2lem11  8292  fin1a2lem13  8294 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-so 4506  df-xp 4886  df-rel 4887  df-rpss 6524
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