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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 2665 | . . 3 | |
2 | 1 | abbidv 2288 | . 2 |
3 | dfint2 3833 | . 2 | |
4 | dfint2 3833 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 cab 2156 wral 2448 cint 3831 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-int 3832 |
This theorem is referenced by: inteqi 3835 inteqd 3836 uniintsnr 3867 rint0 3870 intexr 4136 onintexmid 4557 elreldm 4837 elxp5 5099 1stval2 6134 fundmen 6784 xpsnen 6799 fiintim 6906 elfir 6950 fiinopn 12796 bj-intexr 13943 |
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