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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 1985). (Contributed by NM, 7-Apr-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
hbsb4t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1520 | . . 3 | |
2 | 1 | hbsb4 1985 | . 2 |
3 | spsbim 1815 | . . . . 5 | |
4 | 3 | sps 1517 | . . . 4 |
5 | ax-4 1487 | . . . . . . 7 | |
6 | 5 | sbimi 1737 | . . . . . 6 |
7 | 6 | alimi 1431 | . . . . 5 |
8 | 7 | a1i 9 | . . . 4 |
9 | 4, 8 | imim12d 74 | . . 3 |
10 | 9 | a7s 1430 | . 2 |
11 | 2, 10 | syl5 32 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wal 1329 wsb 1735 |
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-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: nfsb4t 1987 |
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