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Mirrors > Home > MPE Home > Th. List > ineq12 | Structured version Visualization version Unicode version |
Description: Equality theorem for intersection of two classes. (Contributed by NM, 8-May-1994.) |
Ref | Expression |
---|---|
ineq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1 3807 | . 2 | |
2 | ineq2 3808 | . 2 | |
3 | 1, 2 | sylan9eq 2676 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 cin 3573 |
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 df-in 3581 |
This theorem is referenced by: ineq12i 3812 ineq12d 3815 ineqan12d 3816 fnun 5997 undifixp 7944 endisj 8047 sbthlem8 8077 fiin 8328 pm54.43 8826 kmlem9 8980 indistopon 20805 epttop 20813 restbas 20962 ordtbas2 20995 txbas 21370 ptbasin 21380 trfbas2 21647 snfil 21668 fbasrn 21688 trfil2 21691 fmfnfmlem3 21760 ustuqtop2 22046 minveclem3b 23199 isperp 25607 frrlem4 31783 diophin 37336 kelac2lem 37634 |
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