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Mirrors > Home > ILE Home > Th. List > ineq12i | Unicode version |
Description: Equality inference for intersection of two classes. (Contributed by NM, 24-Jun-2004.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
ineq1i.1 | |
ineq12i.2 |
Ref | Expression |
---|---|
ineq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1i.1 | . 2 | |
2 | ineq12i.2 | . 2 | |
3 | ineq12 3242 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 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: undir 3296 difindir 3301 inrab 3318 inrab2 3319 inxp 4643 resindi 4804 resindir 4805 cnvin 4916 rnin 4918 inimass 4925 funtp 5146 imainlem 5174 imain 5175 offres 6001 djuinr 6916 djuin 6917 casefun 6938 exmidfodomrlemim 7025 enq0enq 7207 explecnv 11242 |
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