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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemkuv-2N | Structured version Visualization version GIF version |
Description: Part of proof of Lemma K of [Crawley] p. 118. Value of the sigma2 (p) function, given π. (Contributed by NM, 2-Jul-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
cdlemk2.b | β’ π΅ = (BaseβπΎ) |
cdlemk2.l | β’ β€ = (leβπΎ) |
cdlemk2.j | β’ β¨ = (joinβπΎ) |
cdlemk2.m | β’ β§ = (meetβπΎ) |
cdlemk2.a | β’ π΄ = (AtomsβπΎ) |
cdlemk2.h | β’ π» = (LHypβπΎ) |
cdlemk2.t | β’ π = ((LTrnβπΎ)βπ) |
cdlemk2.r | β’ π = ((trLβπΎ)βπ) |
cdlemk2.s | β’ π = (π β π β¦ (β©π β π (πβπ) = ((π β¨ (π βπ)) β§ ((πβπ) β¨ (π β(π β β‘πΉ)))))) |
cdlemk2.q | β’ π = (πβπΆ) |
cdlemk2.v | β’ π = (π β π β¦ (β©π β π (πβπ) = ((π β¨ (π βπ)) β§ ((πβπ) β¨ (π β(π β β‘πΆ)))))) |
Ref | Expression |
---|---|
cdlemkuv-2N | β’ (πΊ β π β (πβπΊ) = (β©π β π (πβπ) = ((π β¨ (π βπΊ)) β§ ((πβπ) β¨ (π β(πΊ β β‘πΆ)))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdlemk2.b | . 2 β’ π΅ = (BaseβπΎ) | |
2 | cdlemk2.l | . 2 β’ β€ = (leβπΎ) | |
3 | cdlemk2.j | . 2 β’ β¨ = (joinβπΎ) | |
4 | cdlemk2.a | . 2 β’ π΄ = (AtomsβπΎ) | |
5 | cdlemk2.h | . 2 β’ π» = (LHypβπΎ) | |
6 | cdlemk2.t | . 2 β’ π = ((LTrnβπΎ)βπ) | |
7 | cdlemk2.r | . 2 β’ π = ((trLβπΎ)βπ) | |
8 | cdlemk2.m | . 2 β’ β§ = (meetβπΎ) | |
9 | cdlemk2.v | . 2 β’ π = (π β π β¦ (β©π β π (πβπ) = ((π β¨ (π βπ)) β§ ((πβπ) β¨ (π β(π β β‘πΆ)))))) | |
10 | 1, 2, 3, 4, 5, 6, 7, 8, 9 | cdlemksv 40372 | 1 β’ (πΊ β π β (πβπΊ) = (β©π β π (πβπ) = ((π β¨ (π βπΊ)) β§ ((πβπ) β¨ (π β(πΊ β β‘πΆ)))))) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 = wceq 1533 β wcel 2098 β¦ cmpt 5226 β‘ccnv 5671 β ccom 5676 βcfv 6542 β©crio 7370 (class class class)co 7415 Basecbs 17177 lecple 17237 joincjn 18300 meetcmee 18301 Atomscatm 38790 LHypclh 39512 LTrncltrn 39629 trLctrl 39686 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5294 ax-nul 5301 ax-pr 5423 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2931 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3465 df-dif 3943 df-un 3945 df-ss 3957 df-nul 4319 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-br 5144 df-opab 5206 df-mpt 5227 df-id 5570 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-iota 6494 df-fun 6544 df-fv 6550 df-riota 7371 df-ov 7418 |
This theorem is referenced by: (None) |
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