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Mirrors > Home > ILE Home > Th. List > intss1 | Unicode version |
Description: An element of a class includes the intersection of the class. Exercise 4 of [TakeutiZaring] p. 44 (with correction), generalized to classes. (Contributed by NM, 18-Nov-1995.) |
Ref | Expression |
---|---|
intss1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2554 |
. . . 4
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2 | 1 | elint 3612 |
. . 3
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3 | eleq1 2097 |
. . . . . 6
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4 | eleq2 2098 |
. . . . . 6
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5 | 3, 4 | imbi12d 223 |
. . . . 5
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6 | 5 | spcgv 2634 |
. . . 4
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7 | 6 | pm2.43a 45 |
. . 3
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8 | 2, 7 | syl5bi 141 |
. 2
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9 | 8 | ssrdv 2945 |
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-in 2918 df-ss 2925 df-int 3607 |
This theorem is referenced by: intminss 3631 intmin3 3633 intab 3635 int0el 3636 trint0m 3862 inteximm 3894 onnmin 4244 peano5 4264 peano5nni 7698 dfuzi 8124 bj-intabssel 9263 bj-intabssel1 9264 peano5setOLD 9400 |
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