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Mirrors > Home > ILE Home > Th. List > cbvabw | Unicode version |
Description: Version of cbvab 2301 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.) Reduce axiom usage. (Revised by Gino Giotto, 25-Aug-2024.) |
Ref | Expression |
---|---|
cbvabw.1 |
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cbvabw.2 |
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cbvabw.3 |
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Ref | Expression |
---|---|
cbvabw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvabw.1 |
. . . . . 6
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2 | 1 | nfsbv 1947 |
. . . . 5
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3 | equequ2 1713 |
. . . . . . . 8
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4 | 3 | imbi1d 231 |
. . . . . . 7
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5 | 4 | albidv 1824 |
. . . . . 6
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6 | sb6 1886 |
. . . . . 6
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7 | sb6 1886 |
. . . . . 6
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8 | 5, 6, 7 | 3bitr4g 223 |
. . . . 5
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9 | 2, 8 | sbiev 1792 |
. . . 4
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10 | cbvabw.2 |
. . . . . 6
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11 | cbvabw.3 |
. . . . . 6
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12 | 10, 11 | sbiev 1792 |
. . . . 5
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13 | 12 | sbbii 1765 |
. . . 4
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14 | 9, 13 | bitr3i 186 |
. . 3
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15 | df-clab 2164 |
. . 3
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16 | df-clab 2164 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 14, 15, 16 | 3bitr4i 212 |
. 2
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18 | 17 | eqriv 2174 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 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-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 |
This theorem is referenced by: cbvsbcw 2990 |
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