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Mirrors > Home > NFE Home > Th. List > dfsb2 | Unicode version |
Description: An alternate definition of proper substitution that, like df-sb 1649, mixes free and bound variables to avoid distinct variable requirements. (Contributed by NM, 17-Feb-2005.) |
Ref | Expression |
---|---|
dfsb2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 1747 |
. . . 4
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2 | sbequ2 1650 |
. . . . 5
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3 | 2 | sps 1754 |
. . . 4
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4 | orc 374 |
. . . 4
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5 | 1, 3, 4 | ee12an 1363 |
. . 3
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6 | sb4 2053 |
. . . 4
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7 | olc 373 |
. . . 4
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8 | 6, 7 | syl6 29 |
. . 3
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9 | 5, 8 | pm2.61i 156 |
. 2
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10 | sbequ1 1918 |
. . . 4
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11 | 10 | imp 418 |
. . 3
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12 | sb2 2023 |
. . 3
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13 | 11, 12 | jaoi 368 |
. 2
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14 | 9, 13 | impbii 180 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 |
This theorem is referenced by: dfsb3 2056 |
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