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Mirrors > Home > ILE Home > Th. List > fo1st | Unicode version |
Description: The ![]() |
Ref | Expression |
---|---|
fo1st |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2740 |
. . . . . 6
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2 | 1 | snex 4182 |
. . . . 5
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3 | 2 | dmex 4889 |
. . . 4
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4 | 3 | uniex 4434 |
. . 3
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5 | df-1st 6135 |
. . 3
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6 | 4, 5 | fnmpti 5340 |
. 2
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7 | 5 | rnmpt 4871 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | vex 2740 |
. . . . 5
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9 | 8, 8 | opex 4226 |
. . . . . 6
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10 | 8, 8 | op1sta 5106 |
. . . . . . 7
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11 | 10 | eqcomi 2181 |
. . . . . 6
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12 | sneq 3602 |
. . . . . . . . . 10
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13 | 12 | dmeqd 4825 |
. . . . . . . . 9
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14 | 13 | unieqd 3818 |
. . . . . . . 8
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15 | 14 | eqeq2d 2189 |
. . . . . . 7
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16 | 15 | rspcev 2841 |
. . . . . 6
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17 | 9, 11, 16 | mp2an 426 |
. . . . 5
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18 | 8, 17 | 2th 174 |
. . . 4
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19 | 18 | abbi2i 2292 |
. . 3
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20 | 7, 19 | eqtr4i 2201 |
. 2
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21 | df-fo 5218 |
. 2
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22 | 6, 20, 21 | mpbir2an 942 |
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 4206 ax-un 4430 |
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-mpt 4063 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-fun 5214 df-fn 5215 df-fo 5218 df-1st 6135 |
This theorem is referenced by: 1stcof 6158 1stexg 6162 df1st2 6214 1stconst 6216 algrflem 6224 algrflemg 6225 suplocexprlemell 7703 suplocexprlem2b 7704 suplocexprlemlub 7714 upxp 13439 uptx 13441 cnmpt1st 13455 |
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