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Mirrors > Home > HSE Home > Th. List > hvmulcli | Structured version Unicode version |
Description: Closure inference for scalar multiplication. (Contributed by NM, 1-Aug-1999.) (New usage is discouraged.) |
Ref | Expression |
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hvmulcl.1 |
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hvmulcl.2 |
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Ref | Expression |
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hvmulcli |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hvmulcl.1 |
. 2
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2 | hvmulcl.2 |
. 2
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3 | hvmulcl 24552 |
. 2
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4 | 1, 2, 3 | mp2an 672 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4513 ax-nul 4521 ax-pr 4631 ax-hfvmul 24544 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3072 df-sbc 3287 df-csb 3389 df-dif 3431 df-un 3433 df-in 3435 df-ss 3442 df-nul 3738 df-if 3892 df-sn 3978 df-pr 3980 df-op 3984 df-uni 4192 df-iun 4273 df-br 4393 df-opab 4451 df-mpt 4452 df-id 4736 df-xp 4946 df-rel 4947 df-cnv 4948 df-co 4949 df-dm 4950 df-rn 4951 df-iota 5481 df-fun 5520 df-fn 5521 df-f 5522 df-fv 5526 df-ov 6195 |
This theorem is referenced by: hvsubsub4i 24598 hvnegdii 24601 hvsubeq0i 24602 hvsubcan2i 24603 hvaddcani 24604 hvsubaddi 24605 normlem0 24648 normlem5 24653 normlem9 24657 bcseqi 24659 norm-iii-i 24678 norm3difi 24686 normpar2i 24695 polid2i 24696 polidi 24697 h1de2i 25093 pjsubii 25218 eigposi 25377 lnop0 25507 lnopunilem1 25551 lnophmlem2 25558 lnfn0i 25583 |
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