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Mirrors > Home > MPE Home > Th. List > iunxsng | Structured version Visualization version 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 4282 |
. . 3
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2 | iunxsng.1 |
. . . . 5
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3 | 2 | eleq2d 2513 |
. . . 4
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4 | 3 | rexsng 4006 |
. . 3
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5 | 1, 4 | syl5bb 261 |
. 2
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6 | 5 | eqrdv 2448 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ral 2741 df-rex 2742 df-v 3046 df-sbc 3267 df-sn 3968 df-iun 4279 |
This theorem is referenced by: iunxsn 4360 disjiun2 37392 carageniuncllem1 38336 caratheodorylem1 38341 iunxprg 38998 |
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