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Mirrors > Home > ILE Home > Th. List > f1elima | Unicode version |
Description: Membership in the image of a 1-1 map. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
f1elima |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 5419 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | fvelimab 5568 |
. . . 4
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3 | 1, 2 | sylan 283 |
. . 3
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4 | 3 | 3adant2 1016 |
. 2
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5 | ssel 3149 |
. . . . . . . 8
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6 | 5 | impac 381 |
. . . . . . 7
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7 | f1fveq 5767 |
. . . . . . . . . . . 12
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8 | 7 | ancom2s 566 |
. . . . . . . . . . 11
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9 | 8 | biimpd 144 |
. . . . . . . . . 10
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10 | 9 | anassrs 400 |
. . . . . . . . 9
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11 | eleq1 2240 |
. . . . . . . . . 10
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12 | 11 | biimpcd 159 |
. . . . . . . . 9
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13 | 10, 12 | sylan9 409 |
. . . . . . . 8
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14 | 13 | anasss 399 |
. . . . . . 7
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15 | 6, 14 | sylan2 286 |
. . . . . 6
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16 | 15 | anassrs 400 |
. . . . 5
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17 | 16 | rexlimdva 2594 |
. . . 4
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18 | 17 | 3impa 1194 |
. . 3
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19 | eqid 2177 |
. . . 4
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20 | fveq2 5511 |
. . . . . 6
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21 | 20 | eqeq1d 2186 |
. . . . 5
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22 | 21 | rspcev 2841 |
. . . 4
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23 | 19, 22 | mpan2 425 |
. . 3
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24 | 18, 23 | impbid1 142 |
. 2
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25 | 4, 24 | bitrd 188 |
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 4118 ax-pow 4171 ax-pr 4206 |
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-sbc 2963 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-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-res 4635 df-ima 4636 df-iota 5174 df-fun 5214 df-fn 5215 df-f 5216 df-f1 5217 df-fv 5220 |
This theorem is referenced by: f1imass 5769 iseqf1olemnab 10471 fprodssdc 11579 ctinfom 12409 ssnnctlemct 12427 |
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