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Mirrors > Home > MPE Home > Th. List > rightssno | Structured version Visualization version GIF version |
Description: The right set of a surreal number is a subset of the surreals. (Contributed by Scott Fenton, 9-Oct-2024.) |
Ref | Expression |
---|---|
rightssno | ⊢ ( R ‘𝐴) ⊆ No |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rightssold 27719 | . 2 ⊢ ( R ‘𝐴) ⊆ ( O ‘( bday ‘𝐴)) | |
2 | oldssno 27701 | . 2 ⊢ ( O ‘( bday ‘𝐴)) ⊆ No | |
3 | 1, 2 | sstri 3991 | 1 ⊢ ( R ‘𝐴) ⊆ No |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3948 ‘cfv 6543 No csur 27486 bday cbday 27488 O cold 27683 R cright 27686 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-rep 5285 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7729 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-ral 3061 df-rex 3070 df-rmo 3375 df-reu 3376 df-rab 3432 df-v 3475 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-tp 4633 df-op 4635 df-uni 4909 df-int 4951 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7368 df-ov 7415 df-oprab 7416 df-mpo 7417 df-2nd 7980 df-frecs 8272 df-wrecs 8303 df-recs 8377 df-1o 8472 df-2o 8473 df-no 27489 df-slt 27490 df-bday 27491 df-sslt 27627 df-scut 27629 df-made 27687 df-old 27688 df-right 27691 |
This theorem is referenced by: cofcutr 27757 cofcutrtime 27760 lrrecpred 27774 addsproplem2 27800 sleadd1 27819 addsuniflem 27831 negsproplem2 27854 negsproplem5 27857 negsproplem6 27858 negsid 27866 negsunif 27880 mulsrid 27926 mulsproplem5 27933 mulsproplem6 27934 mulsproplem7 27935 mulsproplem8 27936 mulscom 27952 mulsuniflem 27962 addsdilem3 27966 addsdilem4 27967 mulsasslem3 27978 precsexlem8 28025 precsexlem9 28026 precsexlem11 28028 |
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