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Mirrors > Home > MPE Home > Th. List > riotaex | Structured version Visualization version GIF version |
Description: Restricted iota is a set. (Contributed by NM, 15-Sep-2011.) |
Ref | Expression |
---|---|
riotaex | ⊢ (℩𝑥 ∈ 𝐴 𝜓) ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-riota 7103 | . 2 ⊢ (℩𝑥 ∈ 𝐴 𝜓) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜓)) | |
2 | iotaex 6328 | . 2 ⊢ (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜓)) ∈ V | |
3 | 1, 2 | eqeltri 2906 | 1 ⊢ (℩𝑥 ∈ 𝐴 𝜓) ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 396 ∈ wcel 2105 Vcvv 3492 ℩cio 6305 ℩crio 7102 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-nul 5201 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-v 3494 df-sbc 3770 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-sn 4558 df-pr 4560 df-uni 4831 df-iota 6307 df-riota 7103 |
This theorem is referenced by: ordtypelem3 8972 dfac8clem 9446 zorn2lem1 9906 subval 10865 1div0 11287 divval 11288 elq 12338 flval 13152 ceilval2 13198 cjval 14449 sqrtval 14584 sqrtf 14711 cidval 16936 cidfn 16938 lubdm 17577 lubval 17582 glbdm 17590 glbval 17595 grpinvfval 18080 grpinvval 18082 grpinvfn 18083 pj1val 18750 evlsval 20227 q1pval 24674 ig1pval 24693 coeval 24740 quotval 24808 mirfv 26369 mirf 26373 usgredg2v 26936 frgrncvvdeqlem5 28009 1div0apr 28174 gidval 28216 grpoinvval 28227 grpoinvf 28236 pjhval 29101 pjfni 29405 cnlnadjlem5 29775 nmopadjlei 29792 cdj3lem2 30139 xdivval 30522 cvmlift3lem4 32466 scutval 33162 dmscut 33169 fvtransport 33390 finxpreclem4 34557 poimirlem26 34799 lshpkrlem1 36126 lshpkrlem2 36127 lshpkrlem3 36128 trlval 37178 cdleme31fv 37406 cdleme50f 37558 cdlemksv 37860 cdlemkuu 37911 cdlemk40 37933 cdlemk56 37987 cdlemm10N 38134 cdlemn11a 38223 dihval 38248 dihf11lem 38282 dihatlat 38350 dochfl1 38492 mapdhval 38740 hvmapvalvalN 38777 hdmap1vallem 38813 hdmapval 38844 hdmapfnN 38845 hgmapval 38903 hgmapfnN 38904 resubval 39075 mpaaval 39629 wessf1ornlem 41321 |
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