Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > op0le | Structured version Visualization version Unicode version |
Description: Orthoposet zero is less than or equal to any element. (ch0le 28300 analog.) (Contributed by NM, 12-Oct-2011.) |
Ref | Expression |
---|---|
op0le.b | |
op0le.l | |
op0le.z |
Ref | Expression |
---|---|
op0le |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | op0le.b | . 2 | |
2 | eqid 2622 | . 2 | |
3 | op0le.l | . 2 | |
4 | op0le.z | . 2 | |
5 | simpl 473 | . 2 | |
6 | simpr 477 | . 2 | |
7 | eqid 2622 | . . . . 5 | |
8 | 1, 7, 2 | op01dm 34470 | . . . 4 |
9 | 8 | simprd 479 | . . 3 |
10 | 9 | adantr 481 | . 2 |
11 | 1, 2, 3, 4, 5, 6, 10 | p0le 17043 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 class class class wbr 4653 cdm 5114 cfv 5888 cbs 15857 cple 15948 club 16942 cglb 16943 cp0 17037 cops 34459 |
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-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 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-pw 4160 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-id 5024 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-riota 6611 df-ov 6653 df-glb 16975 df-p0 17039 df-oposet 34463 |
This theorem is referenced by: ople0 34474 opnlen0 34475 lub0N 34476 opltn0 34477 olj01 34512 olm01 34523 leatb 34579 1cvratex 34759 llnn0 34802 lplnn0N 34833 lvoln0N 34877 dalemcea 34946 ltrnatb 35423 ltrnmwOLD 35438 tendo0tp 36077 cdlemk39s-id 36228 dia0eldmN 36329 dib0 36453 dih0 36569 dihmeetlem18N 36613 |
Copyright terms: Public domain | W3C validator |