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Mirrors > Home > ILE Home > Th. List > cbvopab | Unicode version |
Description: Rule used to change bound variables in an ordered-pair class abstraction, using implicit substitution. (Contributed by NM, 14-Sep-2003.) |
Ref | Expression |
---|---|
cbvopab.1 |
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cbvopab.2 |
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cbvopab.3 |
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cbvopab.4 |
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cbvopab.5 |
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Ref | Expression |
---|---|
cbvopab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1467 |
. . . . 5
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2 | cbvopab.1 |
. . . . 5
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3 | 1, 2 | nfan 1503 |
. . . 4
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4 | nfv 1467 |
. . . . 5
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5 | cbvopab.2 |
. . . . 5
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6 | 4, 5 | nfan 1503 |
. . . 4
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7 | nfv 1467 |
. . . . 5
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8 | cbvopab.3 |
. . . . 5
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9 | 7, 8 | nfan 1503 |
. . . 4
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10 | nfv 1467 |
. . . . 5
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11 | cbvopab.4 |
. . . . 5
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12 | 10, 11 | nfan 1503 |
. . . 4
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13 | opeq12 3630 |
. . . . . 6
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14 | 13 | eqeq2d 2100 |
. . . . 5
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15 | cbvopab.5 |
. . . . 5
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16 | 14, 15 | anbi12d 458 |
. . . 4
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17 | 3, 6, 9, 12, 16 | cbvex2 1846 |
. . 3
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18 | 17 | abbii 2204 |
. 2
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19 | df-opab 3906 |
. 2
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20 | df-opab 3906 |
. 2
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21 | 18, 19, 20 | 3eqtr4i 2119 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-un 3004 df-sn 3456 df-pr 3457 df-op 3459 df-opab 3906 |
This theorem is referenced by: cbvopabv 3916 opelopabsb 4096 |
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