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Theorem ssunpr 4192
 Description: Possible values for a set sandwiched between another set and it plus a singleton. (Contributed by Mario Carneiro, 2-Jul-2016.)
Assertion
Ref Expression
ssunpr

Proof of Theorem ssunpr
StepHypRef Expression
1 df-pr 4032 . . . . . 6
21uneq2i 3654 . . . . 5
3 unass 3660 . . . . 5
42, 3eqtr4i 2489 . . . 4
54sseq2i 3528 . . 3
65anbi2i 694 . 2
7 ssunsn2 4189 . 2
8 ssunsn 4190 . . 3
9 un23 3662 . . . . . 6
109sseq2i 3528 . . . . 5
1110anbi2i 694 . . . 4
12 ssunsn 4190 . . . 4
134, 9eqtr2i 2487 . . . . . 6
1413eqeq2i 2475 . . . . 5
1514orbi2i 519 . . . 4
1611, 12, 153bitri 271 . . 3
178, 16orbi12i 521 . 2
186, 7, 173bitri 271 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  u.cun 3473  C_wss 3475  {csn 4029  {cpr 4031 This theorem is referenced by:  sspr  4193  sstp  4194 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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