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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 |
Ref | Expression |
---|---|
inteqd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inteqd.1 | . 2 | |
2 | inteq 3821 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 cint 3818 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-int 3819 |
This theorem is referenced by: intprg 3851 op1stbg 4451 onsucmin 4478 elreldm 4824 elxp5 5086 fniinfv 5538 1stval2 6115 2ndval2 6116 fundmen 6763 xpsnen 6778 fiintim 6885 elfi2 6928 fi0 6931 cardcl 7128 isnumi 7129 cardval3ex 7132 carden2bex 7136 clsfval 12642 clsval 12652 |
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