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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 6511 | . 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfiota1 5770 | . 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | nfcxfr 2749 | 1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 383 ∈ wcel 1977 Ⅎwnfc 2738 ℩cio 5766 ℩crio 6510 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-sn 4126 df-uni 4373 df-iota 5768 df-riota 6511 |
This theorem is referenced by: riotaprop 6534 riotass2 6537 riotass 6538 riotaxfrd 6541 lble 10854 riotaneg 10879 zriotaneg 11367 poimirlem26 32605 riotaocN 33514 ltrniotaval 34887 cdlemksv2 35153 cdlemkuv2 35173 cdlemk36 35219 wessf1ornlem 38366 disjinfi 38375 |
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