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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 1509 |
. . . . 5
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2 | cbvopab.1 |
. . . . 5
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3 | 1, 2 | nfan 1545 |
. . . 4
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4 | nfv 1509 |
. . . . 5
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5 | cbvopab.2 |
. . . . 5
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6 | 4, 5 | nfan 1545 |
. . . 4
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7 | nfv 1509 |
. . . . 5
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8 | cbvopab.3 |
. . . . 5
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9 | 7, 8 | nfan 1545 |
. . . 4
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10 | nfv 1509 |
. . . . 5
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11 | cbvopab.4 |
. . . . 5
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12 | 10, 11 | nfan 1545 |
. . . 4
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13 | opeq12 3715 |
. . . . . 6
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14 | 13 | eqeq2d 2152 |
. . . . 5
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15 | cbvopab.5 |
. . . . 5
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16 | 14, 15 | anbi12d 465 |
. . . 4
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17 | 3, 6, 9, 12, 16 | cbvex2 1895 |
. . 3
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18 | 17 | abbii 2256 |
. 2
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19 | df-opab 3998 |
. 2
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20 | df-opab 3998 |
. 2
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21 | 18, 19, 20 | 3eqtr4i 2171 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-opab 3998 |
This theorem is referenced by: cbvopabv 4008 opelopabsb 4190 |
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