![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > elintab | Unicode version |
Description: Membership in the intersection of a class abstraction. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
inteqab.1 |
Ref | Expression |
---|---|
elintab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inteqab.1 | . . 3 | |
2 | 1 | elint 4292 | . 2 |
3 | nfsab1 2446 | . . . 4 | |
4 | nfv 1707 | . . . 4 | |
5 | 3, 4 | nfim 1920 | . . 3 |
6 | nfv 1707 | . . 3 | |
7 | eleq1 2529 | . . . . 5 | |
8 | abid 2444 | . . . . 5 | |
9 | 7, 8 | syl6bb 261 | . . . 4 |
10 | eleq2 2530 | . . . 4 | |
11 | 9, 10 | imbi12d 320 | . . 3 |
12 | 5, 6, 11 | cbval 2021 | . 2 |
13 | 2, 12 | bitri 249 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 <-> wb 184
A. wal 1393 e. wcel 1818 { cab 2442
cvv 3109
|^| cint 4286 |
This theorem is referenced by: elintrab 4298 intmin4 4316 intab 4317 intid 4710 dfom3 8085 dfom5 8088 tc2 8194 dfnn2 10574 efgi 16737 efgi2 16743 mclsax 28929 heibor1lem 30305 brintclab 37763 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-v 3111 df-int 4287 |
Copyright terms: Public domain | W3C validator |