![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 7360 | . 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfiota1 6494 | . 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | nfcxfr 2902 | 1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 397 ∈ wcel 2107 Ⅎwnfc 2884 ℩cio 6490 ℩crio 7359 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ral 3063 df-rex 3072 df-v 3477 df-in 3954 df-ss 3964 df-sn 4628 df-uni 4908 df-iota 6492 df-riota 7360 |
This theorem is referenced by: riotaprop 7388 riotass2 7391 riotass 7392 riotaxfrd 7395 ttrcltr 9707 lble 12162 riotaneg 12189 zriotaneg 12671 nosupbnd1 27197 nosupbnd2 27199 noinfbnd1 27212 noinfbnd2 27214 poimirlem26 36452 riotaocN 38017 ltrniotaval 39390 cdlemksv2 39656 cdlemkuv2 39676 cdlemk36 39722 disjinfi 43824 |
Copyright terms: Public domain | W3C validator |