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Mirrors > Home > ILE Home > Th. List > ssequn2 | Unicode version |
Description: A relationship between subclass and union. (Contributed by NM, 13-Jun-1994.) |
Ref | Expression |
---|---|
ssequn2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssequn1 3156 |
. 2
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2 | uncom 3130 |
. . 3
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3 | 2 | eqeq1i 2092 |
. 2
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4 | 1, 3 | bitri 182 |
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 663 ax-5 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 |
This theorem depends on definitions: df-bi 115 df-tru 1290 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-v 2616 df-un 2990 df-in 2992 df-ss 2999 |
This theorem is referenced by: unabs 3216 pwssunim 4078 pwundifss 4079 oneluni 4225 relresfld 4917 relcoi1 4919 fsnunf 5441 unsnfidcel 6561 exmidfodomrlemim 6748 |
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