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Mirrors > Home > MPE Home > Th. List > Mathboxes > nodmord | Structured version Visualization version Unicode version |
Description: The domain of a surreal has the ordinal property. (Contributed by Scott Fenton, 16-Jun-2011.) |
Ref | Expression |
---|---|
nodmord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nodmon 31803 | . 2 | |
2 | eloni 5733 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cdm 5114 word 5722 con0 5723 csur 31793 |
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-rep 4771 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-tr 4753 df-id 5024 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-ord 5726 df-on 5727 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-no 31796 |
This theorem is referenced by: noseponlem 31817 nosepon 31818 noextend 31819 noextenddif 31821 noextendlt 31822 noextendgt 31823 nolesgn2ores 31825 fvnobday 31829 nosepssdm 31836 nosupbday 31851 nosupres 31853 nosupbnd1lem1 31854 nosupbnd1lem3 31856 nosupbnd1lem5 31858 nosupbnd2lem1 31861 nosupbnd2 31862 noetalem3 31865 |
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