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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 5930 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 1521 | . . . . 5 | |
2 | cbvmpox.1 | . . . . . 6 | |
3 | 2 | nfcri 2306 | . . . . 5 |
4 | 1, 3 | nfan 1558 | . . . 4 |
5 | cbvmpox.3 | . . . . 5 | |
6 | 5 | nfeq2 2324 | . . . 4 |
7 | 4, 6 | nfan 1558 | . . 3 |
8 | nfv 1521 | . . . . 5 | |
9 | nfcv 2312 | . . . . . 6 | |
10 | 9 | nfcri 2306 | . . . . 5 |
11 | 8, 10 | nfan 1558 | . . . 4 |
12 | cbvmpox.4 | . . . . 5 | |
13 | 12 | nfeq2 2324 | . . . 4 |
14 | 11, 13 | nfan 1558 | . . 3 |
15 | nfv 1521 | . . . . 5 | |
16 | cbvmpox.2 | . . . . . 6 | |
17 | 16 | nfcri 2306 | . . . . 5 |
18 | 15, 17 | nfan 1558 | . . . 4 |
19 | cbvmpox.5 | . . . . 5 | |
20 | 19 | nfeq2 2324 | . . . 4 |
21 | 18, 20 | nfan 1558 | . . 3 |
22 | nfv 1521 | . . . 4 | |
23 | cbvmpox.6 | . . . . 5 | |
24 | 23 | nfeq2 2324 | . . . 4 |
25 | 22, 24 | nfan 1558 | . . 3 |
26 | eleq1 2233 | . . . . . 6 | |
27 | 26 | adantr 274 | . . . . 5 |
28 | cbvmpox.7 | . . . . . . 7 | |
29 | 28 | eleq2d 2240 | . . . . . 6 |
30 | eleq1 2233 | . . . . . 6 | |
31 | 29, 30 | sylan9bb 459 | . . . . 5 |
32 | 27, 31 | anbi12d 470 | . . . 4 |
33 | cbvmpox.8 | . . . . 5 | |
34 | 33 | eqeq2d 2182 | . . . 4 |
35 | 32, 34 | anbi12d 470 | . . 3 |
36 | 7, 14, 21, 25, 35 | cbvoprab12 5925 | . 2 |
37 | df-mpo 5856 | . 2 | |
38 | df-mpo 5856 | . 2 | |
39 | 36, 37, 38 | 3eqtr4i 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wnfc 2299 coprab 5852 cmpo 5853 |
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 4105 ax-pow 4158 ax-pr 4192 |
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 3566 df-sn 3587 df-pr 3588 df-op 3590 df-opab 4049 df-oprab 5855 df-mpo 5856 |
This theorem is referenced by: cbvmpo 5930 mpomptsx 6174 dmmpossx 6176 |
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