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Mirrors > Home > MPE Home > Th. List > vcrel | Structured version Visualization version GIF version |
Description: The class of all complex vector spaces is a relation. (Contributed by NM, 17-Mar-2007.) (New usage is discouraged.) |
Ref | Expression |
---|---|
vcrel | β’ Rel CVecOLD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-vc 29543 | . 2 β’ CVecOLD = {β¨π, π β© β£ (π β AbelOp β§ π :(β Γ ran π)βΆran π β§ βπ₯ β ran π((1π π₯) = π₯ β§ βπ¦ β β (βπ§ β ran π(π¦π (π₯ππ§)) = ((π¦π π₯)π(π¦π π§)) β§ βπ§ β β (((π¦ + π§)π π₯) = ((π¦π π₯)π(π§π π₯)) β§ ((π¦ Β· π§)π π₯) = (π¦π (π§π π₯))))))} | |
2 | 1 | relopabiv 5777 | 1 β’ Rel CVecOLD |
Colors of variables: wff setvar class |
Syntax hints: β§ wa 397 β§ w3a 1088 = wceq 1542 β wcel 2107 βwral 3061 Γ cxp 5632 ran crn 5635 Rel wrel 5639 βΆwf 6493 (class class class)co 7358 βcc 11054 1c1 11057 + caddc 11059 Β· cmul 11061 AbelOpcablo 29528 CVecOLDcvc 29542 |
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-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3446 df-in 3918 df-ss 3928 df-opab 5169 df-xp 5640 df-rel 5641 df-vc 29543 |
This theorem is referenced by: vcex 29562 nvvop 29593 phop 29802 |
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