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Mirrors > Home > ILE Home > Th. List > ssiun2 | Unicode version |
Description: Identity law for subset of an indexed union. (Contributed by NM, 12-Oct-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
ssiun2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspe 2425 |
. . . 4
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2 | 1 | ex 114 |
. . 3
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3 | eliun 3740 |
. . 3
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4 | 2, 3 | syl6ibr 161 |
. 2
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5 | 4 | ssrdv 3032 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-in 3006 df-ss 3013 df-iun 3738 |
This theorem is referenced by: ssiun2s 3780 triun 3955 ixpf 6491 |
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