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Mirrors > Home > ILE Home > Th. List > ineq2i | Unicode version |
Description: Equality inference for intersection of two classes. (Contributed by NM, 26-Dec-1993.) |
Ref | Expression |
---|---|
ineq1i.1 |
Ref | Expression |
---|---|
ineq2i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1i.1 | . 2 | |
2 | ineq2 3271 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cin 3070 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 |
This theorem is referenced by: in4 3292 inindir 3294 indif2 3320 difun1 3336 dfrab3ss 3354 dfif3 3487 intunsn 3809 rint0 3810 riin0 3884 res0 4823 resres 4831 resundi 4832 resindi 4834 inres 4836 resiun2 4839 resopab 4863 dfse2 4912 dminxp 4983 imainrect 4984 resdmres 5030 funimacnv 5199 unfiin 6814 sbthlemi5 6849 dmaddpi 7133 dmmulpi 7134 fsumiun 11246 |
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