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Mirrors > Home > MPE Home > Th. List > ralrab | Structured version Visualization version Unicode version |
Description: Universal quantification over a restricted class abstraction. (Contributed by Jeff Madsen, 10-Jun-2010.) |
Ref | Expression |
---|---|
ralab.1 |
Ref | Expression |
---|---|
ralrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralab.1 | . . . . 5 | |
2 | 1 | elrab 3363 | . . . 4 |
3 | 2 | imbi1i 339 | . . 3 |
4 | impexp 462 | . . 3 | |
5 | 3, 4 | bitri 264 | . 2 |
6 | 5 | ralbii2 2978 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wcel 1990 wral 2912 crab 2916 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rab 2921 df-v 3202 |
This theorem is referenced by: frminex 5094 wereu2 5111 weniso 6604 zmin 11784 prmreclem1 15620 lublecllem 16988 mhmeql 17364 ghmeql 17683 pgpfac1lem5 18478 lmhmeql 19055 islindf4 20177 1stcfb 21248 fbssfi 21641 filssufilg 21715 txflf 21810 ptcmplem3 21858 symgtgp 21905 tgpconncompeqg 21915 cnllycmp 22755 ovolgelb 23248 dyadmax 23366 lhop1 23777 radcnvlt1 24172 noextenddif 31821 conway 31910 poimirlem4 33413 poimirlem32 33441 ismblfin 33450 igenval2 33865 glbconN 34663 mgmhmeql 41803 |
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