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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 7388 | . 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
| 2 | nfiota1 6516 | . 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
| 3 | 1, 2 | nfcxfr 2903 | 1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: ∧ wa 395 ∈ wcel 2108 Ⅎwnfc 2890 ℩cio 6512 ℩crio 7387 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-nf 1784 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-ral 3062 df-rex 3071 df-v 3482 df-ss 3968 df-sn 4627 df-uni 4908 df-iota 6514 df-riota 7388 |
| This theorem is referenced by: riotaprop 7415 riotass2 7418 riotass 7419 riotaxfrd 7422 ttrcltr 9756 lble 12220 riotaneg 12247 zriotaneg 12731 nosupbnd1 27759 nosupbnd2 27761 noinfbnd1 27774 noinfbnd2 27776 poimirlem26 37653 riotaocN 39210 ltrniotaval 40583 cdlemksv2 40849 cdlemkuv2 40869 cdlemk36 40915 disjinfi 45197 |
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