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Mirrors > Home > ILE Home > Th. List > isstruct2r | Unicode version |
Description: The property of being a
structure with components in
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
isstruct2r |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 527 |
. 2
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2 | simplr 528 |
. 2
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3 | simprr 531 |
. 2
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4 | simprl 529 |
. . . 4
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5 | 4 | elexd 2752 |
. . 3
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6 | elex 2750 |
. . . 4
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7 | 6 | ad2antrr 488 |
. . 3
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8 | simpr 110 |
. . . . . 6
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9 | 8 | eleq1d 2246 |
. . . . 5
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10 | simpl 109 |
. . . . . . 7
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11 | 10 | difeq1d 3254 |
. . . . . 6
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12 | 11 | funeqd 5240 |
. . . . 5
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13 | 10 | dmeqd 4831 |
. . . . . 6
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14 | 8 | fveq2d 5521 |
. . . . . 6
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15 | 13, 14 | sseq12d 3188 |
. . . . 5
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16 | 9, 12, 15 | 3anbi123d 1312 |
. . . 4
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17 | df-struct 12467 |
. . . 4
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18 | 16, 17 | brabga 4266 |
. . 3
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19 | 5, 7, 18 | syl2anc 411 |
. 2
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20 | 1, 2, 3, 19 | mpbir3and 1180 |
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-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 |
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-rex 2461 df-rab 2464 df-v 2741 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-br 4006 df-opab 4067 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-iota 5180 df-fun 5220 df-fv 5226 df-struct 12467 |
This theorem is referenced by: isstructr 12480 |
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