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Theorem ssunpr 3953
 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 3813 . . . . . 6
21uneq2i 3490 . . . . 5
3 unass 3496 . . . . 5
42, 3eqtr4i 2458 . . . 4
54sseq2i 3365 . . 3
65anbi2i 676 . 2
7 ssunsn2 3950 . 2
8 ssunsn 3951 . . 3
9 un23 3498 . . . . . 6
109sseq2i 3365 . . . . 5
1110anbi2i 676 . . . 4
12 ssunsn 3951 . . . 4
134, 9eqtr2i 2456 . . . . . 6
1413eqeq2i 2445 . . . . 5
1514orbi2i 506 . . . 4
1611, 12, 153bitri 263 . . 3
178, 16orbi12i 508 . 2
186, 7, 173bitri 263 1
 Colors of variables: wff set class Syntax hints:   wb 177   wo 358   wa 359   wceq 1652   cun 3310   wss 3312  csn 3806  cpr 3807 This theorem is referenced by:  sspr  3954  sstp  3955 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813
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