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Mirrors > Home > ILE Home > Th. List > caovcan | Unicode version |
Description: Convert an operation cancellation law to class notation. (Contributed by NM, 20-Aug-1995.) |
Ref | Expression |
---|---|
caovcan.1 |
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caovcan.2 |
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Ref | Expression |
---|---|
caovcan |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 5879 |
. . . 4
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2 | oveq1 5879 |
. . . 4
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3 | 1, 2 | eqeq12d 2192 |
. . 3
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4 | 3 | imbi1d 231 |
. 2
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5 | oveq2 5880 |
. . . 4
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6 | 5 | eqeq1d 2186 |
. . 3
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7 | eqeq1 2184 |
. . 3
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8 | 6, 7 | imbi12d 234 |
. 2
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9 | caovcan.1 |
. . 3
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10 | oveq2 5880 |
. . . . . 6
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11 | 10 | eqeq2d 2189 |
. . . . 5
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12 | eqeq2 2187 |
. . . . 5
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13 | 11, 12 | imbi12d 234 |
. . . 4
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14 | 13 | imbi2d 230 |
. . 3
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15 | caovcan.2 |
. . 3
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16 | 9, 14, 15 | vtocl 2791 |
. 2
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17 | 4, 8, 16 | vtocl2ga 2805 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-iota 5177 df-fv 5223 df-ov 5875 |
This theorem is referenced by: (None) |
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