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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 3241 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 cin 3040 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 |
This theorem is referenced by: in4 3262 inindir 3264 indif2 3290 difun1 3306 dfrab3ss 3324 dfif3 3457 intunsn 3779 rint0 3780 riin0 3854 res0 4793 resres 4801 resundi 4802 resindi 4804 inres 4806 resiun2 4809 resopab 4833 dfse2 4882 dminxp 4953 imainrect 4954 resdmres 5000 funimacnv 5169 unfiin 6782 sbthlemi5 6817 dmaddpi 7101 dmmulpi 7102 fsumiun 11214 |
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