New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  ssunsn Unicode version

Theorem ssunsn 3866
 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
ssunsn

Proof of Theorem ssunsn
StepHypRef Expression
1 ssunsn2 3865 . 2
2 ancom 437 . . . 4
3 eqss 3287 . . . 4
42, 3bitr4i 243 . . 3
5 ancom 437 . . . 4
6 eqss 3287 . . . 4
75, 6bitr4i 243 . . 3
84, 7orbi12i 507 . 2
91, 8bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wo 357   wa 358   wceq 1642   cun 3207   wss 3257  csn 3737 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 This theorem is referenced by:  ssunpr  3868
 Copyright terms: Public domain W3C validator