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Mirrors > Home > ILE Home > Th. List > ssiun2s | Unicode version |
Description: Subset relationship for an indexed union. (Contributed by NM, 26-Oct-2003.) |
Ref | Expression |
---|---|
ssiun2s.1 |
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Ref | Expression |
---|---|
ssiun2s |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2235 |
. 2
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2 | nfcv 2235 |
. . 3
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3 | nfiu1 3782 |
. . 3
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4 | 2, 3 | nfss 3032 |
. 2
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5 | ssiun2s.1 |
. . 3
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6 | 5 | sseq1d 3068 |
. 2
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7 | ssiun2 3795 |
. 2
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8 | 1, 4, 6, 7 | vtoclgaf 2698 |
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 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-v 2635 df-in 3019 df-ss 3026 df-iun 3754 |
This theorem is referenced by: (None) |
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