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Theorem nosgnn0 30086
Description:  (/) is not a surreal sign. (Contributed by Scott Fenton, 16-Jun-2011.)
Assertion
Ref Expression
nosgnn0  |-  -.  (/)  e.  { 1o ,  2o }

Proof of Theorem nosgnn0
StepHypRef Expression
1 1n0 7100 . . . 4  |-  1o  =/=  (/)
21nesymi 2674 . . 3  |-  -.  (/)  =  1o
3 nsuceq0 4899 . . . . 5  |-  suc  1o  =/=  (/)
4 necom 2670 . . . . . 6  |-  ( suc 
1o  =/=  (/)  <->  (/)  =/=  suc  1o )
5 df-2o 7086 . . . . . . 7  |-  2o  =  suc  1o
65neeq2i 2688 . . . . . 6  |-  ( (/)  =/=  2o  <->  (/)  =/=  suc  1o )
74, 6bitr4i 252 . . . . 5  |-  ( suc 
1o  =/=  (/)  <->  (/)  =/=  2o )
83, 7mpbi 208 . . . 4  |-  (/)  =/=  2o
98neii 2600 . . 3  |-  -.  (/)  =  2o
102, 9pm3.2ni 853 . 2  |-  -.  ( (/)  =  1o  \/  (/)  =  2o )
11 0ex 4523 . . 3  |-  (/)  e.  _V
1211elpr 3987 . 2  |-  ( (/)  e.  { 1o ,  2o } 
<->  ( (/)  =  1o  \/  (/)  =  2o ) )
1310, 12mtbir 297 1  |-  -.  (/)  e.  { 1o ,  2o }
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    \/ wo 366    = wceq 1403    e. wcel 1840    =/= wne 2596   (/)c0 3735   {cpr 3971   suc csuc 4821   1oc1o 7078   2oc2o 7079
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378  ax-nul 4522
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-ne 2598  df-v 3058  df-dif 3414  df-un 3416  df-nul 3736  df-sn 3970  df-pr 3972  df-suc 4825  df-1o 7085  df-2o 7086
This theorem is referenced by:  nosgnn0i  30087  sltres  30092  sltso  30097  nodenselem3  30111  nodenselem8  30116
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