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Mirrors > Home > ILE Home > Th. List > suppssof1 | Unicode version |
Description: Formula building theorem for support restrictions: vector operation with left annihilator. (Contributed by Stefan O'Rear, 9-Mar-2015.) |
Ref | Expression |
---|---|
suppssof1.s |
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suppssof1.o |
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suppssof1.a |
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suppssof1.b |
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suppssof1.d |
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Ref | Expression |
---|---|
suppssof1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suppssof1.a |
. . . . . 6
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2 | ffn 5365 |
. . . . . 6
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3 | 1, 2 | syl 14 |
. . . . 5
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4 | suppssof1.b |
. . . . . 6
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5 | ffn 5365 |
. . . . . 6
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6 | 4, 5 | syl 14 |
. . . . 5
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7 | suppssof1.d |
. . . . 5
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8 | inidm 3344 |
. . . . 5
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9 | eqidd 2178 |
. . . . 5
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10 | eqidd 2178 |
. . . . 5
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11 | 3, 6, 7, 7, 8, 9, 10 | offval 6089 |
. . . 4
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12 | 11 | cnveqd 4803 |
. . 3
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13 | 12 | imaeq1d 4969 |
. 2
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14 | 1 | feqmptd 5569 |
. . . . . 6
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15 | 14 | cnveqd 4803 |
. . . . 5
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16 | 15 | imaeq1d 4969 |
. . . 4
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17 | suppssof1.s |
. . . 4
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18 | 16, 17 | eqsstrrd 3192 |
. . 3
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19 | suppssof1.o |
. . 3
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20 | funfvex 5532 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 20 | funfni 5316 |
. . . 4
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22 | 3, 21 | sylan 283 |
. . 3
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23 | 4 | ffvelcdmda 5651 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 18, 19, 22, 23 | suppssov1 6079 |
. 2
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25 | 13, 24 | eqsstrd 3191 |
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-14 2151 ax-ext 2159 ax-coll 4118 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-setind 4536 |
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-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-csb 3058 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-iun 3888 df-br 4004 df-opab 4065 df-mpt 4066 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 df-iota 5178 df-fun 5218 df-fn 5219 df-f 5220 df-f1 5221 df-fo 5222 df-f1o 5223 df-fv 5224 df-ov 5877 df-oprab 5878 df-mpo 5879 df-of 6082 |
This theorem is referenced by: (None) |
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