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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 | |
cbvopab.2 | |
cbvopab.3 | |
cbvopab.4 | |
cbvopab.5 |
Ref | Expression |
---|---|
cbvopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . . . . 5 | |
2 | cbvopab.1 | . . . . 5 | |
3 | 1, 2 | nfan 1497 | . . . 4 |
4 | nfv 1461 | . . . . 5 | |
5 | cbvopab.2 | . . . . 5 | |
6 | 4, 5 | nfan 1497 | . . . 4 |
7 | nfv 1461 | . . . . 5 | |
8 | cbvopab.3 | . . . . 5 | |
9 | 7, 8 | nfan 1497 | . . . 4 |
10 | nfv 1461 | . . . . 5 | |
11 | cbvopab.4 | . . . . 5 | |
12 | 10, 11 | nfan 1497 | . . . 4 |
13 | opeq12 3572 | . . . . . 6 | |
14 | 13 | eqeq2d 2092 | . . . . 5 |
15 | cbvopab.5 | . . . . 5 | |
16 | 14, 15 | anbi12d 456 | . . . 4 |
17 | 3, 6, 9, 12, 16 | cbvex2 1838 | . . 3 |
18 | 17 | abbii 2194 | . 2 |
19 | df-opab 3840 | . 2 | |
20 | df-opab 3840 | . 2 | |
21 | 18, 19, 20 | 3eqtr4i 2111 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wex 1421 cab 2067 cop 3401 copab 3838 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-opab 3840 |
This theorem is referenced by: cbvopabv 3850 opelopabsb 4015 |
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