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Mirrors > Home > ILE Home > Th. List > sbabel | Unicode version |
Description: Theorem to move a substitution in and out of a class abstraction. (Contributed by NM, 27-Sep-2003.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
sbabel.1 |
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Ref | Expression |
---|---|
sbabel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbex 1980 |
. . 3
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2 | sban 1929 |
. . . . 5
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3 | nfv 1509 |
. . . . . . . . . 10
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4 | 3 | sbf 1751 |
. . . . . . . . 9
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5 | 4 | sbrbis 1935 |
. . . . . . . 8
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6 | 5 | sbalv 1981 |
. . . . . . 7
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7 | abeq2 2249 |
. . . . . . . 8
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8 | 7 | sbbii 1739 |
. . . . . . 7
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9 | abeq2 2249 |
. . . . . . 7
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10 | 6, 8, 9 | 3bitr4i 211 |
. . . . . 6
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11 | sbabel.1 |
. . . . . . . 8
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12 | 11 | nfcri 2276 |
. . . . . . 7
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13 | 12 | sbf 1751 |
. . . . . 6
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14 | 10, 13 | anbi12i 456 |
. . . . 5
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15 | 2, 14 | bitri 183 |
. . . 4
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16 | 15 | exbii 1585 |
. . 3
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17 | 1, 16 | bitri 183 |
. 2
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18 | df-clel 2136 |
. . 3
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19 | 18 | sbbii 1739 |
. 2
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20 | df-clel 2136 |
. 2
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21 | 17, 19, 20 | 3bitr4i 211 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 |
This theorem is referenced by: (None) |
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