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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 |
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ineq12i.2 |
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Ref | Expression |
---|---|
ineq12i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1i.1 |
. 2
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2 | ineq12i.2 |
. 2
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3 | ineq12 3332 |
. 2
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4 | 1, 2, 3 | mp2an 426 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2740 df-in 3136 |
This theorem is referenced by: undir 3386 difindir 3391 inrab 3408 inrab2 3409 inxp 4762 resindi 4923 resindir 4924 cnvin 5037 rnin 5039 inimass 5046 funtp 5270 imainlem 5298 imain 5299 offres 6136 djuinr 7062 djuin 7063 casefun 7084 exmidfodomrlemim 7200 enq0enq 7430 explecnv 11513 |
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