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Mirrors > Home > ILE Home > Th. List > ressval3d | Unicode version |
Description: Value of structure restriction, deduction version. (Contributed by AV, 14-Mar-2020.) (Revised by Jim Kingdon, 17-Jan-2025.) |
Ref | Expression |
---|---|
ressval3d.r |
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ressval3d.b |
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ressval3d.e |
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ressval3d.s |
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ressval3d.f |
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ressval3d.d |
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ressval3d.u |
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Ref | Expression |
---|---|
ressval3d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressval3d.r |
. . 3
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2 | ressval3d.s |
. . . 4
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3 | ressval3d.b |
. . . . . 6
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4 | basfn 12511 |
. . . . . . 7
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5 | 2 | elexd 2750 |
. . . . . . 7
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6 | funfvex 5530 |
. . . . . . . 8
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7 | 6 | funfni 5314 |
. . . . . . 7
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8 | 4, 5, 7 | sylancr 414 |
. . . . . 6
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9 | 3, 8 | eqeltrid 2264 |
. . . . 5
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10 | ressval3d.u |
. . . . 5
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11 | 9, 10 | ssexd 4142 |
. . . 4
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12 | ressvalsets 12515 |
. . . 4
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13 | 2, 11, 12 | syl2anc 411 |
. . 3
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14 | 1, 13 | eqtrid 2222 |
. 2
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15 | ressval3d.e |
. . . . 5
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16 | 15 | a1i 9 |
. . . 4
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17 | df-ss 3142 |
. . . . . 6
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18 | 10, 17 | sylib 122 |
. . . . 5
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19 | 3 | ineq2i 3333 |
. . . . 5
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20 | 18, 19 | eqtr3di 2225 |
. . . 4
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21 | 16, 20 | opeq12d 3786 |
. . 3
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22 | 21 | oveq2d 5887 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 14, 22 | eqtr4d 2213 |
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-in1 614 ax-in2 615 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 4120 ax-pow 4173 ax-pr 4208 ax-un 4432 ax-setind 4535 ax-cnex 7898 ax-resscn 7899 ax-1re 7901 ax-addrcl 7904 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 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-ne 2348 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4003 df-opab 4064 df-mpt 4065 df-id 4292 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-rn 4636 df-res 4637 df-iota 5176 df-fun 5216 df-fn 5217 df-fv 5222 df-ov 5874 df-oprab 5875 df-mpo 5876 df-inn 8915 df-ndx 12456 df-slot 12457 df-base 12459 df-sets 12460 df-iress 12461 |
This theorem is referenced by: (None) |
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