Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > cbvoprab12 | Unicode version |
Description: Rule used to change first two bound variables in an operation abstraction, using implicit substitution. (Contributed by NM, 21-Feb-2004.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
cbvoprab12.1 | |
cbvoprab12.2 | |
cbvoprab12.3 | |
cbvoprab12.4 | |
cbvoprab12.5 |
Ref | Expression |
---|---|
cbvoprab12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . . . . 5 | |
2 | cbvoprab12.1 | . . . . 5 | |
3 | 1, 2 | nfan 1545 | . . . 4 |
4 | nfv 1508 | . . . . 5 | |
5 | cbvoprab12.2 | . . . . 5 | |
6 | 4, 5 | nfan 1545 | . . . 4 |
7 | nfv 1508 | . . . . 5 | |
8 | cbvoprab12.3 | . . . . 5 | |
9 | 7, 8 | nfan 1545 | . . . 4 |
10 | nfv 1508 | . . . . 5 | |
11 | cbvoprab12.4 | . . . . 5 | |
12 | 10, 11 | nfan 1545 | . . . 4 |
13 | opeq12 3744 | . . . . . 6 | |
14 | 13 | eqeq2d 2169 | . . . . 5 |
15 | cbvoprab12.5 | . . . . 5 | |
16 | 14, 15 | anbi12d 465 | . . . 4 |
17 | 3, 6, 9, 12, 16 | cbvex2 1902 | . . 3 |
18 | 17 | opabbii 4032 | . 2 |
19 | dfoprab2 5869 | . 2 | |
20 | dfoprab2 5869 | . 2 | |
21 | 18, 19, 20 | 3eqtr4i 2188 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wnf 1440 wex 1472 cop 3563 copab 4025 coprab 5826 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-opab 4027 df-oprab 5829 |
This theorem is referenced by: cbvoprab12v 5897 cbvmpox 5900 dfoprab4f 6142 fmpox 6149 tposoprab 6228 |
Copyright terms: Public domain | W3C validator |