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Mirrors > Home > ILE Home > Th. List > lidrideqd | Unicode version |
Description: If there is a left and
right identity element for any binary operation
(group operation) ![]() |
Ref | Expression |
---|---|
lidrideqd.l |
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lidrideqd.r |
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lidrideqd.li |
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lidrideqd.ri |
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Ref | Expression |
---|---|
lidrideqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 5895 |
. . . 4
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2 | id 19 |
. . . 4
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3 | 1, 2 | eqeq12d 2202 |
. . 3
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4 | lidrideqd.ri |
. . 3
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5 | lidrideqd.l |
. . 3
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6 | 3, 4, 5 | rspcdva 2858 |
. 2
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7 | oveq2 5896 |
. . . 4
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8 | id 19 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | eqeq12d 2202 |
. . 3
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10 | lidrideqd.li |
. . 3
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11 | lidrideqd.r |
. . 3
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12 | 9, 10, 11 | rspcdva 2858 |
. 2
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13 | 6, 12 | eqtr3d 2222 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-iota 5190 df-fv 5236 df-ov 5891 |
This theorem is referenced by: lidrididd 12819 |
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