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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 6518 | . 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | nfcxfr 2901 | 1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 395 ∈ wcel 2106 Ⅎwnfc 2888 ℩cio 6514 ℩crio 7387 |
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 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-ex 1777 df-nf 1781 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-ral 3060 df-rex 3069 df-v 3480 df-ss 3980 df-sn 4632 df-uni 4913 df-iota 6516 df-riota 7388 |
This theorem is referenced by: riotaprop 7415 riotass2 7418 riotass 7419 riotaxfrd 7422 ttrcltr 9754 lble 12218 riotaneg 12245 zriotaneg 12729 nosupbnd1 27774 nosupbnd2 27776 noinfbnd1 27789 noinfbnd2 27791 poimirlem26 37633 riotaocN 39191 ltrniotaval 40564 cdlemksv2 40830 cdlemkuv2 40850 cdlemk36 40896 disjinfi 45135 |
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