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Mirrors > Home > ILE Home > Th. List > cbvmpo | Unicode version |
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. (Contributed by NM, 17-Dec-2013.) |
Ref | Expression |
---|---|
cbvmpo.1 | |
cbvmpo.2 | |
cbvmpo.3 | |
cbvmpo.4 | |
cbvmpo.5 |
Ref | Expression |
---|---|
cbvmpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2312 | . 2 | |
2 | nfcv 2312 | . 2 | |
3 | cbvmpo.1 | . 2 | |
4 | cbvmpo.2 | . 2 | |
5 | cbvmpo.3 | . 2 | |
6 | cbvmpo.4 | . 2 | |
7 | eqidd 2171 | . 2 | |
8 | cbvmpo.5 | . 2 | |
9 | 1, 2, 3, 4, 5, 6, 7, 8 | cbvmpox 5929 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wnfc 2299 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: cbvmpov 5931 fnmpoovd 6192 fmpoco 6193 xpf1o 6819 cnmpt2t 13048 |
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