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Mirrors > Home > ILE Home > Th. List > inteq | Unicode version |
Description: Equality law for intersection. (Contributed by NM, 13-Sep-1999.) |
Ref | Expression |
---|---|
inteq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq 2652 | . . 3 | |
2 | 1 | abbidv 2275 | . 2 |
3 | dfint2 3809 | . 2 | |
4 | dfint2 3809 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 cab 2143 wral 2435 cint 3807 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-int 3808 |
This theorem is referenced by: inteqi 3811 inteqd 3812 uniintsnr 3843 rint0 3846 intexr 4111 onintexmid 4531 elreldm 4811 elxp5 5073 1stval2 6100 fundmen 6748 xpsnen 6763 fiintim 6870 elfir 6914 fiinopn 12389 bj-intexr 13470 |
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