Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > nosgnn0i | Structured version Visualization version Unicode version |
Description: If is a surreal sign, then it is not null. (Contributed by Scott Fenton, 3-Aug-2011.) |
Ref | Expression |
---|---|
nosgnn0i.1 |
Ref | Expression |
---|---|
nosgnn0i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nosgnn0 31811 | . . 3 | |
2 | nosgnn0i.1 | . . . 4 | |
3 | eleq1 2689 | . . . 4 | |
4 | 2, 3 | mpbiri 248 | . . 3 |
5 | 1, 4 | mto 188 | . 2 |
6 | 5 | neir 2797 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 wne 2794 c0 3915 cpr 4179 c1o 7553 c2o 7554 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-v 3202 df-dif 3577 df-un 3579 df-nul 3916 df-sn 4178 df-pr 4180 df-suc 5729 df-1o 7560 df-2o 7561 |
This theorem is referenced by: sltres 31815 noextenddif 31821 nolesgn2ores 31825 nosepnelem 31830 nosepdmlem 31833 nolt02o 31845 nosupbnd1lem3 31856 nosupbnd1lem5 31858 nosupbnd2lem1 31861 |
Copyright terms: Public domain | W3C validator |