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Mirrors > Home > MPE Home > Th. List > nfriota1 | Structured version Visualization version GIF version |
Description: The abstraction variable in a restricted iota descriptor isn't free. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfriota1 | ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-riota 7113 | . 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfiota1 6315 | . 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | nfcxfr 2975 | 1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 398 ∈ wcel 2110 Ⅎwnfc 2961 ℩cio 6311 ℩crio 7112 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-v 3496 df-in 3942 df-ss 3951 df-sn 4567 df-uni 4838 df-iota 6313 df-riota 7113 |
This theorem is referenced by: riotaprop 7140 riotass2 7143 riotass 7144 riotaxfrd 7147 lble 11592 riotaneg 11619 zriotaneg 12095 nosupbnd1 33214 nosupbnd2 33216 poimirlem26 34917 riotaocN 36344 ltrniotaval 37716 cdlemksv2 37982 cdlemkuv2 38002 cdlemk36 38048 disjinfi 41452 |
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