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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 |
Ref | Expression |
---|---|
iunxsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliun 4524 | . . 3 | |
2 | iunxsng.1 | . . . . 5 | |
3 | 2 | eleq2d 2687 | . . . 4 |
4 | 3 | rexsng 4219 | . . 3 |
5 | 1, 4 | syl5bb 272 | . 2 |
6 | 5 | eqrdv 2620 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 wrex 2913 csn 4177 ciun 4520 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 df-sn 4178 df-iun 4522 |
This theorem is referenced by: iunxsn 4603 iunxprg 4607 disjiun2 39226 carageniuncllem1 40735 caratheodorylem1 40740 |
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