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Mirrors > Home > MPE Home > Th. List > Mathboxes > op1cl | Structured version Visualization version Unicode version |
Description: An orthoposet has a unit element. (helch 28100 analog.) (Contributed by NM, 22-Oct-2011.) |
Ref | Expression |
---|---|
op1cl.b | |
op1cl.u |
Ref | Expression |
---|---|
op1cl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | op1cl.b | . . 3 | |
2 | eqid 2622 | . . 3 | |
3 | op1cl.u | . . 3 | |
4 | 1, 2, 3 | p1val 17042 | . 2 |
5 | id 22 | . . 3 | |
6 | eqid 2622 | . . . . 5 | |
7 | 1, 2, 6 | op01dm 34470 | . . . 4 |
8 | 7 | simpld 475 | . . 3 |
9 | 1, 2, 5, 8 | lubcl 16985 | . 2 |
10 | 4, 9 | eqeltrd 2701 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 cdm 5114 cfv 5888 cbs 15857 club 16942 cglb 16943 cp1 17038 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-lub 16974 df-p1 17040 df-oposet 34463 |
This theorem is referenced by: op1le 34479 glb0N 34480 opoc1 34489 opoc0 34490 olm11 34514 olm12 34515 ncvr1 34559 hlhgt2 34675 hl0lt1N 34676 hl2at 34691 athgt 34742 1cvrco 34758 1cvrjat 34761 pmap1N 35053 pol1N 35196 lhp2lt 35287 lhpexnle 35292 dih1 36575 dih1rn 36576 dih1cnv 36577 dihglb2 36631 dochocss 36655 dihjatc 36706 |
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