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Mirrors > Home > ILE Home > Th. List > inteqd | Unicode version |
Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003.) |
Ref | Expression |
---|---|
inteqd.1 |
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Ref | Expression |
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inteqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inteqd.1 |
. 2
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2 | inteq 3845 |
. 2
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3 | 1, 2 | syl 14 |
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-ral 2460 df-int 3843 |
This theorem is referenced by: intprg 3875 op1stbg 4475 onsucmin 4502 elreldm 4848 elxp5 5112 fniinfv 5569 1stval2 6149 2ndval2 6150 fundmen 6799 xpsnen 6814 fiintim 6921 elfi2 6964 fi0 6967 cardcl 7173 isnumi 7174 cardval3ex 7177 carden2bex 7181 clsfval 13234 clsval 13244 |
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