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Mirrors > Home > ILE Home > Th. List > nfsb4t | Unicode version |
Description: A variable not free remains so after substitution with a distinct variable (closed form of hbsb4 1999). (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 4-Oct-2016.) (Proof rewritten by Jim Kingdon, 9-May-2018.) |
Ref | Expression |
---|---|
nfsb4t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnf1 1531 | . . . . 5 | |
2 | 1 | nfal 1563 | . . . 4 |
3 | nfnae 1709 | . . . 4 | |
4 | 2, 3 | nfan 1552 | . . 3 |
5 | df-nf 1448 | . . . . . 6 | |
6 | 5 | albii 1457 | . . . . 5 |
7 | hbsb4t 2000 | . . . . 5 | |
8 | 6, 7 | sylbi 120 | . . . 4 |
9 | 8 | imp 123 | . . 3 |
10 | 4, 9 | nfd 1510 | . 2 |
11 | 10 | ex 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wal 1340 wnf 1447 wsb 1749 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 |
This theorem is referenced by: dvelimdf 2003 |
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