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Mirrors > Home > ILE Home > Th. List > abid | Unicode version |
Description: Simplification of class abstraction notation when the free and bound variables are identical. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
abid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clab 2164 |
. 2
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2 | sbid 1774 |
. 2
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3 | 1, 2 | bitri 184 |
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-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 |
This theorem depends on definitions: df-bi 117 df-sb 1763 df-clab 2164 |
This theorem is referenced by: abeq2 2286 abeq2i 2288 abeq1i 2289 abeq2d 2290 abid2f 2345 elabgt 2878 elabgf 2879 ralab2 2901 rexab2 2903 sbccsbg 3086 sbccsb2g 3087 ss2ab 3223 abn0r 3447 abn0m 3448 tpid3g 3707 eluniab 3821 elintab 3855 iunab 3933 iinab 3948 intexabim 4152 iinexgm 4154 opm 4234 finds2 4600 dmmrnm 4846 sniota 5207 eusvobj2 5860 eloprabga 5961 indpi 7340 elabgf0 14411 |
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