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Mirrors > Home > ILE Home > Th. List > cbvmptf | Unicode version |
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable conditions. (Contributed by Thierry Arnoux, 9-Mar-2017.) |
Ref | Expression |
---|---|
cbvmptf.1 | |
cbvmptf.2 | |
cbvmptf.3 | |
cbvmptf.4 | |
cbvmptf.5 |
Ref | Expression |
---|---|
cbvmptf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . . . 4 | |
2 | cbvmptf.1 | . . . . . 6 | |
3 | 2 | nfcri 2293 | . . . . 5 |
4 | nfs1v 1919 | . . . . 5 | |
5 | 3, 4 | nfan 1545 | . . . 4 |
6 | eleq1w 2218 | . . . . 5 | |
7 | sbequ12 1751 | . . . . 5 | |
8 | 6, 7 | anbi12d 465 | . . . 4 |
9 | 1, 5, 8 | cbvopab1 4040 | . . 3 |
10 | cbvmptf.2 | . . . . . 6 | |
11 | 10 | nfcri 2293 | . . . . 5 |
12 | cbvmptf.3 | . . . . . . 7 | |
13 | 12 | nfeq2 2311 | . . . . . 6 |
14 | 13 | nfsb 1926 | . . . . 5 |
15 | 11, 14 | nfan 1545 | . . . 4 |
16 | nfv 1508 | . . . 4 | |
17 | eleq1w 2218 | . . . . 5 | |
18 | cbvmptf.4 | . . . . . . 7 | |
19 | 18 | nfeq2 2311 | . . . . . 6 |
20 | cbvmptf.5 | . . . . . . 7 | |
21 | 20 | eqeq2d 2169 | . . . . . 6 |
22 | 19, 21 | sbhypf 2761 | . . . . 5 |
23 | 17, 22 | anbi12d 465 | . . . 4 |
24 | 15, 16, 23 | cbvopab1 4040 | . . 3 |
25 | 9, 24 | eqtri 2178 | . 2 |
26 | df-mpt 4030 | . 2 | |
27 | df-mpt 4030 | . 2 | |
28 | 25, 26, 27 | 3eqtr4i 2188 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wsb 1742 wcel 2128 wnfc 2286 copab 4027 cmpt 4028 |
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-ext 2139 |
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-sn 3567 df-pr 3568 df-op 3570 df-opab 4029 df-mpt 4030 |
This theorem is referenced by: resmptf 4919 |
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