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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 1508 | . . . . 5 | |
2 | cbvopab.1 | . . . . 5 | |
3 | 1, 2 | nfan 1544 | . . . 4 |
4 | nfv 1508 | . . . . 5 | |
5 | cbvopab.2 | . . . . 5 | |
6 | 4, 5 | nfan 1544 | . . . 4 |
7 | nfv 1508 | . . . . 5 | |
8 | cbvopab.3 | . . . . 5 | |
9 | 7, 8 | nfan 1544 | . . . 4 |
10 | nfv 1508 | . . . . 5 | |
11 | cbvopab.4 | . . . . 5 | |
12 | 10, 11 | nfan 1544 | . . . 4 |
13 | opeq12 3702 | . . . . . 6 | |
14 | 13 | eqeq2d 2149 | . . . . 5 |
15 | cbvopab.5 | . . . . 5 | |
16 | 14, 15 | anbi12d 464 | . . . 4 |
17 | 3, 6, 9, 12, 16 | cbvex2 1892 | . . 3 |
18 | 17 | abbii 2253 | . 2 |
19 | df-opab 3985 | . 2 | |
20 | df-opab 3985 | . 2 | |
21 | 18, 19, 20 | 3eqtr4i 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wex 1468 cab 2123 cop 3525 copab 3983 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-opab 3985 |
This theorem is referenced by: cbvopabv 3995 opelopabsb 4177 |
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