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Mirrors > Home > MPE Home > Th. List > dfsb2 | Structured version Visualization version Unicode version |
Description: An alternate definition of proper substitution that, like df-sb 1808, 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 1947 |
. . . 4
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2 | sbequ2 1809 |
. . . . 5
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3 | 2 | sps 1953 |
. . . 4
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4 | orc 391 |
. . . 4
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5 | 1, 3, 4 | syl6an 552 |
. . 3
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6 | sb4 2197 |
. . . 4
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7 | olc 390 |
. . . 4
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8 | 6, 7 | syl6 34 |
. . 3
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9 | 5, 8 | pm2.61i 169 |
. 2
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10 | sbequ1 2092 |
. . . 4
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11 | 10 | imp 435 |
. . 3
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12 | sb2 2193 |
. . 3
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13 | 11, 12 | jaoi 385 |
. 2
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14 | 9, 13 | impbii 192 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-12 1943 ax-13 2101 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-ex 1674 df-nf 1678 df-sb 1808 |
This theorem is referenced by: dfsb3 2213 |
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