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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 2560 |
. 2
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2 | sbcexg 2807 |
. . . 4
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3 | sbcang 2800 |
. . . . . 6
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4 | sbcalg 2805 |
. . . . . . . . 9
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5 | sbcbig 2803 |
. . . . . . . . . . 11
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6 | sbcg 2821 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | bibi1d 222 |
. . . . . . . . . . 11
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8 | 5, 7 | bitrd 177 |
. . . . . . . . . 10
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9 | 8 | albidv 1702 |
. . . . . . . . 9
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10 | 4, 9 | bitrd 177 |
. . . . . . . 8
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11 | abeq2 2143 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 11 | sbcbii 2812 |
. . . . . . . 8
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13 | abeq2 2143 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 10, 12, 13 | 3bitr4g 212 |
. . . . . . 7
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15 | sbcabel.1 |
. . . . . . . . 9
![]() ![]() ![]() ![]() | |
16 | 15 | nfcri 2169 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
17 | 16 | sbcgf 2819 |
. . . . . . 7
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18 | 14, 17 | anbi12d 442 |
. . . . . 6
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19 | 3, 18 | bitrd 177 |
. . . . 5
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20 | 19 | exbidv 1703 |
. . . 4
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21 | 2, 20 | bitrd 177 |
. . 3
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22 | df-clel 2033 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 22 | sbcbii 2812 |
. . 3
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24 | df-clel 2033 |
. . 3
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25 | 21, 23, 24 | 3bitr4g 212 |
. 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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-sbc 2759 |
This theorem is referenced by: csbexga 3876 |
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