![]() |
Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > cdleme43frv1snN | Structured version Visualization version GIF version |
Description: Value of β¦π / π β¦π when Β¬ π β€ (π β¨ π). (Contributed by NM, 30-Mar-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
cdlemefr27.b | β’ π΅ = (BaseβπΎ) |
cdlemefr27.l | β’ β€ = (leβπΎ) |
cdlemefr27.j | β’ β¨ = (joinβπΎ) |
cdlemefr27.m | β’ β§ = (meetβπΎ) |
cdlemefr27.a | β’ π΄ = (AtomsβπΎ) |
cdlemefr27.h | β’ π» = (LHypβπΎ) |
cdlemefr27.u | β’ π = ((π β¨ π) β§ π) |
cdlemefr27.c | β’ πΆ = ((π β¨ π) β§ (π β¨ ((π β¨ π ) β§ π))) |
cdlemefr27.n | β’ π = if(π β€ (π β¨ π), πΌ, πΆ) |
cdleme43fr.x | β’ π = ((π β¨ π) β§ (π β¨ ((π β¨ π ) β§ π))) |
Ref | Expression |
---|---|
cdleme43frv1snN | β’ ((π β π΄ β§ Β¬ π β€ (π β¨ π)) β β¦π / π β¦π = π) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdlemefr27.c | . 2 β’ πΆ = ((π β¨ π) β§ (π β¨ ((π β¨ π ) β§ π))) | |
2 | cdlemefr27.n | . 2 β’ π = if(π β€ (π β¨ π), πΌ, πΆ) | |
3 | cdleme43fr.x | . 2 β’ π = ((π β¨ π) β§ (π β¨ ((π β¨ π ) β§ π))) | |
4 | 1, 2, 3 | cdleme31sn2 38881 | 1 β’ ((π β π΄ β§ Β¬ π β€ (π β¨ π)) β β¦π / π β¦π = π) |
Colors of variables: wff setvar class |
Syntax hints: Β¬ wn 3 β wi 4 β§ wa 397 = wceq 1542 β wcel 2107 β¦csb 3860 ifcif 4491 class class class wbr 5110 βcfv 6501 (class class class)co 7362 Basecbs 17090 lecple 17147 joincjn 18207 meetcmee 18208 Atomscatm 37754 LHypclh 38476 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-rab 3411 df-v 3450 df-sbc 3745 df-csb 3861 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-if 4492 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-br 5111 df-iota 6453 df-fv 6509 df-ov 7365 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |