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Mirrors > Home > MPE Home > Th. List > Mathboxes > diadmleN | Structured version Visualization version GIF version |
Description: A member of domain of the partial isomorphism A is under the fiducial hyperplane. (Contributed by NM, 5-Dec-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
diadmle.l | β’ β€ = (leβπΎ) |
diadmle.h | β’ π» = (LHypβπΎ) |
diadmle.i | β’ πΌ = ((DIsoAβπΎ)βπ) |
Ref | Expression |
---|---|
diadmleN | β’ (((πΎ β π β§ π β π») β§ π β dom πΌ) β π β€ π) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2737 | . . 3 β’ (BaseβπΎ) = (BaseβπΎ) | |
2 | diadmle.l | . . 3 β’ β€ = (leβπΎ) | |
3 | diadmle.h | . . 3 β’ π» = (LHypβπΎ) | |
4 | diadmle.i | . . 3 β’ πΌ = ((DIsoAβπΎ)βπ) | |
5 | 1, 2, 3, 4 | diaeldm 39528 | . 2 β’ ((πΎ β π β§ π β π») β (π β dom πΌ β (π β (BaseβπΎ) β§ π β€ π))) |
6 | 5 | simplbda 501 | 1 β’ (((πΎ β π β§ π β π») β§ π β dom πΌ) β π β€ π) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β§ wa 397 = wceq 1542 β wcel 2107 class class class wbr 5110 dom cdm 5638 βcfv 6501 Basecbs 17090 lecple 17147 LHypclh 38476 DIsoAcdia 39520 |
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 ax-rep 5247 ax-sep 5261 ax-nul 5268 ax-pr 5389 |
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-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-ral 3066 df-rex 3075 df-reu 3357 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-iun 4961 df-br 5111 df-opab 5173 df-mpt 5194 df-id 5536 df-xp 5644 df-rel 5645 df-cnv 5646 df-co 5647 df-dm 5648 df-rn 5649 df-res 5650 df-ima 5651 df-iota 6453 df-fun 6503 df-fn 6504 df-f 6505 df-f1 6506 df-fo 6507 df-f1o 6508 df-fv 6509 df-disoa 39521 |
This theorem is referenced by: diaocN 39617 doca2N 39618 djajN 39629 |
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