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Mirrors > Home > ILE Home > Th. List > cbvmpt2x | Unicode version |
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. This version of cbvmpt2 5603 allows to be a function of . (Contributed by NM, 29-Dec-2014.) |
Ref | Expression |
---|---|
cbvmpt2x.1 | |
cbvmpt2x.2 | |
cbvmpt2x.3 | |
cbvmpt2x.4 | |
cbvmpt2x.5 | |
cbvmpt2x.6 | |
cbvmpt2x.7 | |
cbvmpt2x.8 |
Ref | Expression |
---|---|
cbvmpt2x |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . . . . 5 | |
2 | cbvmpt2x.1 | . . . . . 6 | |
3 | 2 | nfcri 2213 | . . . . 5 |
4 | 1, 3 | nfan 1497 | . . . 4 |
5 | cbvmpt2x.3 | . . . . 5 | |
6 | 5 | nfeq2 2230 | . . . 4 |
7 | 4, 6 | nfan 1497 | . . 3 |
8 | nfv 1461 | . . . . 5 | |
9 | nfcv 2219 | . . . . . 6 | |
10 | 9 | nfcri 2213 | . . . . 5 |
11 | 8, 10 | nfan 1497 | . . . 4 |
12 | cbvmpt2x.4 | . . . . 5 | |
13 | 12 | nfeq2 2230 | . . . 4 |
14 | 11, 13 | nfan 1497 | . . 3 |
15 | nfv 1461 | . . . . 5 | |
16 | cbvmpt2x.2 | . . . . . 6 | |
17 | 16 | nfcri 2213 | . . . . 5 |
18 | 15, 17 | nfan 1497 | . . . 4 |
19 | cbvmpt2x.5 | . . . . 5 | |
20 | 19 | nfeq2 2230 | . . . 4 |
21 | 18, 20 | nfan 1497 | . . 3 |
22 | nfv 1461 | . . . 4 | |
23 | cbvmpt2x.6 | . . . . 5 | |
24 | 23 | nfeq2 2230 | . . . 4 |
25 | 22, 24 | nfan 1497 | . . 3 |
26 | eleq1 2141 | . . . . . 6 | |
27 | 26 | adantr 270 | . . . . 5 |
28 | cbvmpt2x.7 | . . . . . . 7 | |
29 | 28 | eleq2d 2148 | . . . . . 6 |
30 | eleq1 2141 | . . . . . 6 | |
31 | 29, 30 | sylan9bb 449 | . . . . 5 |
32 | 27, 31 | anbi12d 456 | . . . 4 |
33 | cbvmpt2x.8 | . . . . 5 | |
34 | 33 | eqeq2d 2092 | . . . 4 |
35 | 32, 34 | anbi12d 456 | . . 3 |
36 | 7, 14, 21, 25, 35 | cbvoprab12 5598 | . 2 |
37 | df-mpt2 5537 | . 2 | |
38 | df-mpt2 5537 | . 2 | |
39 | 36, 37, 38 | 3eqtr4i 2111 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wcel 1433 wnfc 2206 coprab 5533 cmpt2 5534 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-opab 3840 df-oprab 5536 df-mpt2 5537 |
This theorem is referenced by: cbvmpt2 5603 mpt2mptsx 5843 dmmpt2ssx 5845 |
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