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Mirrors > Home > MPE Home > Th. List > elabg | Structured version Visualization version Unicode version |
Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. (Contributed by NM, 14-Apr-1995.) |
Ref | Expression |
---|---|
elabg.1 |
Ref | Expression |
---|---|
elabg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2764 | . 2 | |
2 | nfv 1843 | . 2 | |
3 | elabg.1 | . 2 | |
4 | 1, 2, 3 | elabgf 3348 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wcel 1990 cab 2608 |
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-v 3202 |
This theorem is referenced by: elab2g 3353 intmin3 4505 elxpi 5130 finds 7092 wfrlem15 7429 elfi 8319 inficl 8331 dffi3 8337 scott0 8749 elgch 9444 nqpr 9836 hashf1lem1 13239 cshword 13537 trclublem 13734 cotrtrclfv 13753 dfiso2 16432 lubval 16984 glbval 16997 efgcpbllemb 18168 frgpuplem 18185 lspsn 19002 mpfind 19536 pf1ind 19719 eltg 20761 eltg2 20762 islocfin 21320 fbssfi 21641 isewlk 26498 elabreximd 29348 abfmpunirn 29452 orvcval 30519 nosupfv 31852 nosupres 31853 nosupbnd1lem3 31856 nosupbnd1lem5 31858 poimirlem3 33412 poimirlem25 33434 islshpkrN 34407 setindtrs 37592 rngunsnply 37743 frege55lem1c 38210 nzss 38516 elabrexg 39206 ismea 40668 afvelrnb 41243 afvelrnb0 41244 cshword2 41437 |
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