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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 1521 | . . . 4 | |
2 | cbvmptf.1 | . . . . . 6 | |
3 | 2 | nfcri 2306 | . . . . 5 |
4 | nfs1v 1932 | . . . . 5 | |
5 | 3, 4 | nfan 1558 | . . . 4 |
6 | eleq1w 2231 | . . . . 5 | |
7 | sbequ12 1764 | . . . . 5 | |
8 | 6, 7 | anbi12d 470 | . . . 4 |
9 | 1, 5, 8 | cbvopab1 4062 | . . 3 |
10 | cbvmptf.2 | . . . . . 6 | |
11 | 10 | nfcri 2306 | . . . . 5 |
12 | cbvmptf.3 | . . . . . . 7 | |
13 | 12 | nfeq2 2324 | . . . . . 6 |
14 | 13 | nfsb 1939 | . . . . 5 |
15 | 11, 14 | nfan 1558 | . . . 4 |
16 | nfv 1521 | . . . 4 | |
17 | eleq1w 2231 | . . . . 5 | |
18 | cbvmptf.4 | . . . . . . 7 | |
19 | 18 | nfeq2 2324 | . . . . . 6 |
20 | cbvmptf.5 | . . . . . . 7 | |
21 | 20 | eqeq2d 2182 | . . . . . 6 |
22 | 19, 21 | sbhypf 2779 | . . . . 5 |
23 | 17, 22 | anbi12d 470 | . . . 4 |
24 | 15, 16, 23 | cbvopab1 4062 | . . 3 |
25 | 9, 24 | eqtri 2191 | . 2 |
26 | df-mpt 4052 | . 2 | |
27 | df-mpt 4052 | . 2 | |
28 | 25, 26, 27 | 3eqtr4i 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wsb 1755 wcel 2141 wnfc 2299 copab 4049 cmpt 4050 |
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-ext 2152 |
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-sn 3589 df-pr 3590 df-op 3592 df-opab 4051 df-mpt 4052 |
This theorem is referenced by: resmptf 4941 |
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