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Mirrors > Home > MPE Home > Th. List > chfnrn | Structured version Visualization version Unicode version |
Description: The range of a choice function (a function that chooses an element from each member of its domain) is included in the union of its domain. (Contributed by NM, 31-Aug-1999.) |
Ref | Expression |
---|---|
chfnrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvelrnb 6243 | . . . . 5 | |
2 | 1 | biimpd 219 | . . . 4 |
3 | eleq1 2689 | . . . . . . 7 | |
4 | 3 | biimpcd 239 | . . . . . 6 |
5 | 4 | ralimi 2952 | . . . . 5 |
6 | rexim 3008 | . . . . 5 | |
7 | 5, 6 | syl 17 | . . . 4 |
8 | 2, 7 | sylan9 689 | . . 3 |
9 | eluni2 4440 | . . 3 | |
10 | 8, 9 | syl6ibr 242 | . 2 |
11 | 10 | ssrdv 3609 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 wss 3574 cuni 4436 crn 5115 wfn 5883 cfv 5888 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 |
This theorem is referenced by: stoweidlem59 40276 |
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