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Mirrors > Home > ILE Home > Th. List > caovcang | Unicode version |
Description: Convert an operation cancellation law to class notation. (Contributed by NM, 20-Aug-1995.) (Revised by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovcang.1 |
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Ref | Expression |
---|---|
caovcang |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovcang.1 |
. . 3
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2 | 1 | ralrimivvva 2396 |
. 2
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3 | oveq1 5462 |
. . . . 5
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4 | oveq1 5462 |
. . . . 5
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5 | 3, 4 | eqeq12d 2051 |
. . . 4
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6 | 5 | bibi1d 222 |
. . 3
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7 | oveq2 5463 |
. . . . 5
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8 | 7 | eqeq1d 2045 |
. . . 4
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9 | eqeq1 2043 |
. . . 4
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10 | 8, 9 | bibi12d 224 |
. . 3
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11 | oveq2 5463 |
. . . . 5
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12 | 11 | eqeq2d 2048 |
. . . 4
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13 | eqeq2 2046 |
. . . 4
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14 | 12, 13 | bibi12d 224 |
. . 3
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15 | 6, 10, 14 | rspc3v 2659 |
. 2
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16 | 2, 15 | mpan9 265 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-iota 4810 df-fv 4853 df-ov 5458 |
This theorem is referenced by: caovcand 5605 |
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