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Theorem nosgnn0i 25614
 Description: If is a surreal sign, then it is not null. (Contributed by Scott Fenton, 3-Aug-2011.)
Hypothesis
Ref Expression
nosgnn0i.1
Assertion
Ref Expression
nosgnn0i

Proof of Theorem nosgnn0i
StepHypRef Expression
1 nosgnn0 25613 . . 3
2 nosgnn0i.1 . . . 4
3 eleq1 2496 . . . 4
42, 3mpbiri 225 . . 3
51, 4mto 169 . 2
6 df-ne 2601 . 2
75, 6mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1652   wcel 1725   wne 2599  c0 3628  cpr 3815  c1o 6717  c2o 6718 This theorem is referenced by:  sltres  25619  nobndlem2  25648  nobndlem4  25650  nobndlem5  25651  nobndlem6  25652  nobndlem8  25654 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 2417  ax-nul 4338 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-nul 3629  df-sn 3820  df-pr 3821  df-suc 4587  df-1o 6724  df-2o 6725
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