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Theorem sorpssun 6530
 Description: A chain of sets is closed under binary union. (Contributed by Mario Carneiro, 16-May-2015.)
Assertion
Ref Expression
sorpssun []

Proof of Theorem sorpssun
StepHypRef Expression
1 simprr 735 . . 3 []
2 ssequn1 3518 . . . 4
3 eleq1 2497 . . . 4
42, 3sylbi 189 . . 3
51, 4syl5ibrcom 215 . 2 []
6 simprl 734 . . 3 []
7 ssequn2 3521 . . . 4
8 eleq1 2497 . . . 4
97, 8sylbi 189 . . 3
106, 9syl5ibrcom 215 . 2 []
11 sorpssi 6529 . 2 []
125, 10, 11mpjaod 372 1 []
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726   cun 3319   wss 3321   wor 4503   [] crpss 6522 This theorem is referenced by:  finsschain  7414  lbsextlem2  16232  lbsextlem3  16233  filssufilg  17944 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 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 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 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-pss 3337  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-br 4214  df-opab 4268  df-so 4505  df-xp 4885  df-rel 4886  df-rpss 6523
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