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Mirrors > Home > MPE Home > Th. List > clmlmod | Structured version Visualization version Unicode version |
Description: A complex module is a left module. (Contributed by Mario Carneiro, 16-Oct-2015.) |
Ref | Expression |
---|---|
clmlmod |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2453 |
. . 3
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2 | eqid 2453 |
. . 3
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3 | 1, 2 | isclm 22107 |
. 2
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4 | 3 | simp1bi 1024 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-nul 4537 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-rab 2748 df-v 3049 df-sbc 3270 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-nul 3734 df-if 3884 df-sn 3971 df-pr 3973 df-op 3977 df-uni 4202 df-br 4406 df-iota 5549 df-fv 5593 df-ov 6298 df-clm 22106 |
This theorem is referenced by: clmgrp 22111 clmabl 22112 clmring 22113 clmfgrp 22114 clmvsass 22130 clmvsdir 22131 clmvs1 22132 clm0vs 22133 clmvneg1 22134 clmvsneg 22135 clmsubdir 22137 zlmclm 22138 ttgbtwnid 24926 ttgcontlem1 24927 |
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