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Mirrors > Home > ILE Home > Th. List > cbvoprab3 | Unicode version |
Description: Rule used to change the third bound variable in an operation abstraction, using implicit substitution. (Contributed by NM, 22-Aug-2013.) |
Ref | Expression |
---|---|
cbvoprab3.1 | |
cbvoprab3.2 | |
cbvoprab3.3 |
Ref | Expression |
---|---|
cbvoprab3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1521 | . . . . . 6 | |
2 | cbvoprab3.1 | . . . . . 6 | |
3 | 1, 2 | nfan 1558 | . . . . 5 |
4 | 3 | nfex 1630 | . . . 4 |
5 | 4 | nfex 1630 | . . 3 |
6 | nfv 1521 | . . . . . 6 | |
7 | cbvoprab3.2 | . . . . . 6 | |
8 | 6, 7 | nfan 1558 | . . . . 5 |
9 | 8 | nfex 1630 | . . . 4 |
10 | 9 | nfex 1630 | . . 3 |
11 | cbvoprab3.3 | . . . . 5 | |
12 | 11 | anbi2d 461 | . . . 4 |
13 | 12 | 2exbidv 1861 | . . 3 |
14 | 5, 10, 13 | cbvopab2 4063 | . 2 |
15 | dfoprab2 5900 | . 2 | |
16 | dfoprab2 5900 | . 2 | |
17 | 14, 15, 16 | 3eqtr4i 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wnf 1453 wex 1485 cop 3586 copab 4049 coprab 5854 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-opab 4051 df-oprab 5857 |
This theorem is referenced by: cbvoprab3v 5930 tposoprab 6259 erovlem 6605 |
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