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Theorem ssunpr 3868
 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 3742 . . . . . 6
21uneq2i 3415 . . . . 5
3 unass 3420 . . . . 5
42, 3eqtr4i 2376 . . . 4
54sseq2i 3296 . . 3
65anbi2i 675 . 2
7 ssunsn2 3865 . 2
8 ssunsn 3866 . . 3
9 un23 3422 . . . . . 6
109sseq2i 3296 . . . . 5
1110anbi2i 675 . . . 4
12 ssunsn 3866 . . . 4
134, 9eqtr2i 2374 . . . . . 6
1413eqeq2i 2363 . . . . 5
1514orbi2i 505 . . . 4
1611, 12, 153bitri 262 . . 3
178, 16orbi12i 507 . 2
186, 7, 173bitri 262 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wo 357   wa 358   wceq 1642   cun 3207   wss 3257  csn 3737  cpr 3738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742 This theorem is referenced by:  sspr  3869  sstp  3870
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