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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 1948). (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 4-Oct-2016.) (Proof rewritten by Jim Kingdon, 9-May-2018.) |
Ref | Expression |
---|---|
nfsb4t |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnf1 1491 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | nfal 1523 |
. . . 4
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3 | nfnae 1668 |
. . . 4
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4 | 2, 3 | nfan 1512 |
. . 3
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5 | df-nf 1405 |
. . . . . 6
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6 | 5 | albii 1414 |
. . . . 5
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7 | hbsb4t 1949 |
. . . . 5
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8 | 6, 7 | sylbi 120 |
. . . 4
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9 | 8 | imp 123 |
. . 3
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10 | 4, 9 | nfd 1471 |
. 2
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11 | 10 | ex 114 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 |
This theorem is referenced by: dvelimdf 1952 |
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