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Mirrors > Home > ILE Home > Th. List > iunxsng | Unicode version |
Description: A singleton index picks out an instance of an indexed union's argument. (Contributed by Mario Carneiro, 25-Jun-2016.) |
Ref | Expression |
---|---|
iunxsng.1 |
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Ref | Expression |
---|---|
iunxsng |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliun 3902 |
. . 3
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2 | iunxsng.1 |
. . . . 5
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3 | 2 | eleq2d 2257 |
. . . 4
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4 | 3 | rexsng 3645 |
. . 3
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5 | 1, 4 | bitrid 192 |
. 2
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6 | 5 | eqrdv 2185 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-sbc 2975 df-sn 3610 df-iun 3900 |
This theorem is referenced by: iunxsn 3975 iunxprg 3979 rdgisuc1 6398 oasuc 6478 omsuc 6486 |
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