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Mirrors > Home > ILE Home > Th. List > cbvralsv | Unicode version |
Description: Change bound variable by using a substitution. (Contributed by NM, 20-Nov-2005.) (Revised by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
cbvralsv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . . 3 | |
2 | nfs1v 1856 | . . 3 | |
3 | sbequ12 1694 | . . 3 | |
4 | 1, 2, 3 | cbvral 2573 | . 2 |
5 | nfv 1461 | . . . 4 | |
6 | 5 | nfsb 1863 | . . 3 |
7 | nfv 1461 | . . 3 | |
8 | sbequ 1761 | . . 3 | |
9 | 6, 7, 8 | cbvral 2573 | . 2 |
10 | 4, 9 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 103 wsb 1685 wral 2348 |
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-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 |
This theorem is referenced by: sbralie 2590 rspsbc 2896 ralxpf 4500 |
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