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Mirrors > Home > ILE Home > Th. List > cbvmpox | Unicode version |
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. This version of cbvmpo 5850 allows to be a function of . (Contributed by NM, 29-Dec-2014.) |
Ref | Expression |
---|---|
cbvmpox.1 | |
cbvmpox.2 | |
cbvmpox.3 | |
cbvmpox.4 | |
cbvmpox.5 | |
cbvmpox.6 | |
cbvmpox.7 | |
cbvmpox.8 |
Ref | Expression |
---|---|
cbvmpox |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . . . . 5 | |
2 | cbvmpox.1 | . . . . . 6 | |
3 | 2 | nfcri 2275 | . . . . 5 |
4 | 1, 3 | nfan 1544 | . . . 4 |
5 | cbvmpox.3 | . . . . 5 | |
6 | 5 | nfeq2 2293 | . . . 4 |
7 | 4, 6 | nfan 1544 | . . 3 |
8 | nfv 1508 | . . . . 5 | |
9 | nfcv 2281 | . . . . . 6 | |
10 | 9 | nfcri 2275 | . . . . 5 |
11 | 8, 10 | nfan 1544 | . . . 4 |
12 | cbvmpox.4 | . . . . 5 | |
13 | 12 | nfeq2 2293 | . . . 4 |
14 | 11, 13 | nfan 1544 | . . 3 |
15 | nfv 1508 | . . . . 5 | |
16 | cbvmpox.2 | . . . . . 6 | |
17 | 16 | nfcri 2275 | . . . . 5 |
18 | 15, 17 | nfan 1544 | . . . 4 |
19 | cbvmpox.5 | . . . . 5 | |
20 | 19 | nfeq2 2293 | . . . 4 |
21 | 18, 20 | nfan 1544 | . . 3 |
22 | nfv 1508 | . . . 4 | |
23 | cbvmpox.6 | . . . . 5 | |
24 | 23 | nfeq2 2293 | . . . 4 |
25 | 22, 24 | nfan 1544 | . . 3 |
26 | eleq1 2202 | . . . . . 6 | |
27 | 26 | adantr 274 | . . . . 5 |
28 | cbvmpox.7 | . . . . . . 7 | |
29 | 28 | eleq2d 2209 | . . . . . 6 |
30 | eleq1 2202 | . . . . . 6 | |
31 | 29, 30 | sylan9bb 457 | . . . . 5 |
32 | 27, 31 | anbi12d 464 | . . . 4 |
33 | cbvmpox.8 | . . . . 5 | |
34 | 33 | eqeq2d 2151 | . . . 4 |
35 | 32, 34 | anbi12d 464 | . . 3 |
36 | 7, 14, 21, 25, 35 | cbvoprab12 5845 | . 2 |
37 | df-mpo 5779 | . 2 | |
38 | df-mpo 5779 | . 2 | |
39 | 36, 37, 38 | 3eqtr4i 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wnfc 2268 coprab 5775 cmpo 5776 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-oprab 5778 df-mpo 5779 |
This theorem is referenced by: cbvmpo 5850 mpomptsx 6095 dmmpossx 6097 |
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