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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 3331 |
. 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 2739 df-in 3135 |
This theorem is referenced by: undir 3385 difindir 3390 inrab 3407 inrab2 3408 inxp 4756 resindi 4917 resindir 4918 cnvin 5031 rnin 5033 inimass 5040 funtp 5264 imainlem 5292 imain 5293 offres 6129 djuinr 7055 djuin 7056 casefun 7077 exmidfodomrlemim 7193 enq0enq 7408 explecnv 11484 |
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