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Mirrors > Home > NFE 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 3974 |
. . 3
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2 | iunxsng.1 |
. . . . 5
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3 | 2 | eleq2d 2420 |
. . . 4
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4 | 3 | rexsng 3767 |
. . 3
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5 | 1, 4 | syl5bb 248 |
. 2
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6 | 5 | eqrdv 2351 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ral 2620 df-rex 2621 df-v 2862 df-sbc 3048 df-sn 3742 df-iun 3972 |
This theorem is referenced by: iunxsn 4046 |
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