Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > cbvoprab1 | Unicode version |
Description: Rule used to change first bound variable in an operation abstraction, using implicit substitution. (Contributed by NM, 20-Dec-2008.) (Revised by Mario Carneiro, 5-Dec-2016.) |
Ref | Expression |
---|---|
cbvoprab1.1 | |
cbvoprab1.2 | |
cbvoprab1.3 |
Ref | Expression |
---|---|
cbvoprab1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . . . . . 6 | |
2 | cbvoprab1.1 | . . . . . 6 | |
3 | 1, 2 | nfan 1529 | . . . . 5 |
4 | 3 | nfex 1601 | . . . 4 |
5 | nfv 1493 | . . . . . 6 | |
6 | cbvoprab1.2 | . . . . . 6 | |
7 | 5, 6 | nfan 1529 | . . . . 5 |
8 | 7 | nfex 1601 | . . . 4 |
9 | opeq1 3675 | . . . . . . 7 | |
10 | 9 | eqeq2d 2129 | . . . . . 6 |
11 | cbvoprab1.3 | . . . . . 6 | |
12 | 10, 11 | anbi12d 464 | . . . . 5 |
13 | 12 | exbidv 1781 | . . . 4 |
14 | 4, 8, 13 | cbvex 1714 | . . 3 |
15 | 14 | opabbii 3965 | . 2 |
16 | dfoprab2 5786 | . 2 | |
17 | dfoprab2 5786 | . 2 | |
18 | 15, 16, 17 | 3eqtr4i 2148 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wnf 1421 wex 1453 cop 3500 copab 3958 coprab 5743 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-opab 3960 df-oprab 5746 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |