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Mirrors > Home > ILE Home > Th. List > sbcabel | Unicode version |
Description: Interchange class substitution and class abstraction. (Contributed by NM, 5-Nov-2005.) |
Ref | Expression |
---|---|
sbcabel.1 |
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Ref | Expression |
---|---|
sbcabel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2630 |
. 2
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2 | sbcexg 2893 |
. . . 4
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3 | sbcang 2882 |
. . . . . 6
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4 | sbcalg 2891 |
. . . . . . . . 9
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5 | sbcbig 2885 |
. . . . . . . . . . 11
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6 | sbcg 2908 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | bibi1d 231 |
. . . . . . . . . . 11
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8 | 5, 7 | bitrd 186 |
. . . . . . . . . 10
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9 | 8 | albidv 1752 |
. . . . . . . . 9
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10 | 4, 9 | bitrd 186 |
. . . . . . . 8
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11 | abeq2 2196 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 11 | sbcbii 2898 |
. . . . . . . 8
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13 | abeq2 2196 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 10, 12, 13 | 3bitr4g 221 |
. . . . . . 7
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15 | sbcabel.1 |
. . . . . . . . 9
![]() ![]() ![]() ![]() | |
16 | 15 | nfcri 2222 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
17 | 16 | sbcgf 2906 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 14, 17 | anbi12d 457 |
. . . . . 6
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19 | 3, 18 | bitrd 186 |
. . . . 5
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20 | 19 | exbidv 1753 |
. . . 4
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21 | 2, 20 | bitrd 186 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | df-clel 2084 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 22 | sbcbii 2898 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | df-clel 2084 |
. . 3
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25 | 21, 23, 24 | 3bitr4g 221 |
. 2
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26 | 1, 25 | syl 14 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-sbc 2841 |
This theorem is referenced by: csbexga 3967 |
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