Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > pmap1N | Structured version Visualization version Unicode version |
Description: Value of the projective map of a Hilbert lattice at lattice unit. Part of Theorem 15.5.1 of [MaedaMaeda] p. 62. (Contributed by NM, 22-Oct-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pmap1.u | |
pmap1.a | |
pmap1.m |
Ref | Expression |
---|---|
pmap1N |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . . . 4 | |
2 | pmap1.u | . . . 4 | |
3 | 1, 2 | op1cl 34472 | . . 3 |
4 | eqid 2622 | . . . 4 | |
5 | pmap1.a | . . . 4 | |
6 | pmap1.m | . . . 4 | |
7 | 1, 4, 5, 6 | pmapval 35043 | . . 3 |
8 | 3, 7 | mpdan 702 | . 2 |
9 | 1, 5 | atbase 34576 | . . . . 5 |
10 | 1, 4, 2 | ople1 34478 | . . . . 5 |
11 | 9, 10 | sylan2 491 | . . . 4 |
12 | 11 | ralrimiva 2966 | . . 3 |
13 | rabid2 3118 | . . 3 | |
14 | 12, 13 | sylibr 224 | . 2 |
15 | 8, 14 | eqtr4d 2659 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 wral 2912 crab 2916 class class class wbr 4653 cfv 5888 cbs 15857 cple 15948 cp1 17038 cops 34459 catm 34550 cpmap 34783 |
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 df-ats 34554 df-pmap 34790 |
This theorem is referenced by: pmapglb2N 35057 pmapglb2xN 35058 |
Copyright terms: Public domain | W3C validator |