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Mirrors > Home > MPE Home > Th. List > max2 | Structured version Visualization version Unicode version |
Description: A number is less than or equal to the maximum of it and another. (Contributed by NM, 3-Apr-2005.) |
Ref | Expression |
---|---|
max2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexr 10085 | . 2 | |
2 | rexr 10085 | . 2 | |
3 | xrmax2 12007 | . 2 | |
4 | 1, 2, 3 | syl2an 494 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 cif 4086 class class class wbr 4653 cr 9935 cxr 10073 cle 10075 |
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-8 1992 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-pow 4843 ax-pr 4906 ax-un 6949 ax-cnex 9992 ax-resscn 9993 ax-pre-lttri 10010 ax-pre-lttrn 10011 |
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-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 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-pw 4160 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-po 5035 df-so 5036 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-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-xr 10078 df-ltxr 10079 df-le 10080 |
This theorem is referenced by: lemaxle 12026 z2ge 12029 ssfzunsnext 12386 uzsup 12662 expmulnbnd 12996 discr1 13000 rexuzre 14092 caubnd 14098 limsupgre 14212 limsupbnd2 14214 rlim3 14229 lo1bdd2 14255 o1lo1 14268 rlimclim1 14276 lo1mul 14358 rlimno1 14384 cvgrat 14615 ruclem10 14968 bitsfzo 15157 1arith 15631 evth 22758 ioombl1lem4 23329 itg2monolem3 23519 itgle 23576 ibladdlem 23586 plyaddlem1 23969 coeaddlem 24005 o1cxp 24701 cxp2lim 24703 cxploglim2 24705 ftalem1 24799 ftalem2 24800 chtppilim 25164 dchrisumlem3 25180 ostth2lem2 25323 ostth2lem3 25324 ostth2lem4 25325 ostth3 25327 knoppndvlem18 32520 ibladdnclem 33466 ftc1anclem5 33489 irrapxlem4 37389 irrapxlem5 37390 rexabslelem 39645 uzublem 39657 max2d 39688 climsuse 39840 limsupubuzlem 39944 limsupmnfuzlem 39958 limsupequzmptlem 39960 limsupre3uzlem 39967 liminflelimsuplem 40007 ioodvbdlimc1lem2 40147 ioodvbdlimc2lem 40149 hoidifhspdmvle 40834 |
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