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Mirrors > Home > ILE Home > Th. List > ovexg | Unicode version |
Description: Evaluating a set operation at two sets gives a set. (Contributed by Jim Kingdon, 19-Aug-2021.) |
Ref | Expression |
---|---|
ovexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 5871 |
. 2
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2 | simp2 998 |
. . 3
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3 | opexg 4224 |
. . . 4
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4 | 3 | 3adant2 1016 |
. . 3
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5 | fvexg 5529 |
. . 3
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6 | 2, 4, 5 | syl2anc 411 |
. 2
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7 | 1, 6 | eqeltrid 2264 |
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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-cnv 4630 df-dm 4632 df-rn 4633 df-iota 5173 df-fv 5219 df-ov 5871 |
This theorem is referenced by: mapxpen 6841 plusfvalg 12661 plusffng 12663 grpsubval 12796 mulgval 12862 mulgfng 12863 mulg1 12866 mulgnnp1 12867 mulgnndir 12887 metrest 13639 |
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