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Mirrors > Home > MPE Home > Th. List > f1elima | Structured version Visualization version 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 5763 |
. . . 4
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2 | fvelimab 5905 |
. . . 4
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3 | 1, 2 | sylan 478 |
. . 3
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4 | 3 | 3adant2 1028 |
. 2
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5 | ssel 3394 |
. . . . . . . 8
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6 | 5 | impac 631 |
. . . . . . 7
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7 | f1fveq 6149 |
. . . . . . . . . . . 12
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8 | 7 | ancom2s 816 |
. . . . . . . . . . 11
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9 | 8 | biimpd 212 |
. . . . . . . . . 10
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10 | 9 | anassrs 658 |
. . . . . . . . 9
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11 | eleq1 2518 |
. . . . . . . . . 10
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12 | 11 | biimpcd 232 |
. . . . . . . . 9
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13 | 10, 12 | sylan9 667 |
. . . . . . . 8
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14 | 13 | anasss 657 |
. . . . . . 7
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15 | 6, 14 | sylan2 481 |
. . . . . 6
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16 | 15 | anassrs 658 |
. . . . 5
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17 | 16 | rexlimdva 2852 |
. . . 4
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18 | 17 | 3impa 1205 |
. . 3
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19 | eqid 2452 |
. . . 4
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20 | fveq2 5848 |
. . . . . 6
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21 | 20 | eqeq1d 2454 |
. . . . 5
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22 | 21 | rspcev 3118 |
. . . 4
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23 | 19, 22 | mpan2 682 |
. . 3
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24 | 18, 23 | impbid1 208 |
. 2
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25 | 4, 24 | bitrd 261 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pr 4612 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3015 df-sbc 3236 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-if 3850 df-sn 3937 df-pr 3939 df-op 3943 df-uni 4169 df-br 4375 df-opab 4434 df-id 4727 df-xp 4818 df-rel 4819 df-cnv 4820 df-co 4821 df-dm 4822 df-rn 4823 df-res 4824 df-ima 4825 df-iota 5525 df-fun 5563 df-fn 5564 df-f 5565 df-f1 5566 df-fv 5569 |
This theorem is referenced by: f1imass 6151 domunfican 7831 acndom2 8472 hashf1lem1 12613 f1omvdconj 17098 gsumzaddlem 17565 lindfmm 19396 axcontlem10 25015 eupath2lem3 25719 ismtyima 32137 |
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