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Mirrors > Home > MPE Home > Th. List > eluz1i | Structured version Visualization version Unicode version |
Description: Membership in an upper set of integers. (Contributed by NM, 5-Sep-2005.) |
Ref | Expression |
---|---|
eluz.1 |
Ref | Expression |
---|---|
eluz1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluz.1 | . 2 | |
2 | eluz1 11691 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wcel 1990 class class class wbr 4653 cfv 5888 cle 10075 cz 11377 cuz 11687 |
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-sep 4781 ax-nul 4789 ax-pr 4906 ax-cnex 9992 ax-resscn 9993 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 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-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 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-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-neg 10269 df-z 11378 df-uz 11688 |
This theorem is referenced by: eluzaddi 11714 eluzsubi 11715 eluz2b1 11759 fz0to4untppr 12442 faclbnd4lem1 13080 climcndslem1 14581 ef01bndlem 14914 sin01bnd 14915 cos01bnd 14916 sin01gt0 14920 dvradcnv 24175 bposlem3 25011 bposlem4 25012 bposlem5 25013 bposlem9 25017 istrkg3ld 25360 axlowdimlem16 25837 ballotlem2 30550 nn0prpwlem 32317 jm2.20nn 37564 stoweidlem17 40234 wallispilem4 40285 nn0o1gt2ALTV 41605 |
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