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Mirrors > Home > ILE Home > Th. List > hbsb4t | Unicode version |
Description: A variable not free remains so after substitution with a distinct variable (closed form of hbsb4 1929). (Contributed by NM, 7-Apr-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
hbsb4t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1473 | . . 3 | |
2 | 1 | hbsb4 1929 | . 2 |
3 | spsbim 1764 | . . . . 5 | |
4 | 3 | sps 1470 | . . . 4 |
5 | ax-4 1440 | . . . . . . 7 | |
6 | 5 | sbimi 1687 | . . . . . 6 |
7 | 6 | alimi 1384 | . . . . 5 |
8 | 7 | a1i 9 | . . . 4 |
9 | 4, 8 | imim12d 73 | . . 3 |
10 | 9 | a7s 1383 | . 2 |
11 | 2, 10 | syl5 32 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wal 1282 wsb 1685 |
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-in2 577 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 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 |
This theorem is referenced by: nfsb4t 1931 |
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