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Mirrors > Home > MPE Home > Th. List > imaco | Structured version Visualization version Unicode version |
Description: Image of the composition of two classes. (Contributed by Jason Orendorff, 12-Dec-2006.) |
Ref | Expression |
---|---|
imaco |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2743 |
. . 3
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2 | vex 3048 |
. . . 4
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3 | 2 | elima 5173 |
. . 3
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4 | rexcom4 3067 |
. . . . 5
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5 | r19.41v 2942 |
. . . . . 6
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6 | 5 | exbii 1718 |
. . . . 5
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7 | 4, 6 | bitri 253 |
. . . 4
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8 | 2 | elima 5173 |
. . . . 5
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9 | vex 3048 |
. . . . . . 7
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10 | 9, 2 | brco 5005 |
. . . . . 6
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11 | 10 | rexbii 2889 |
. . . . 5
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12 | 8, 11 | bitri 253 |
. . . 4
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13 | vex 3048 |
. . . . . . 7
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14 | 13 | elima 5173 |
. . . . . 6
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15 | 14 | anbi1i 701 |
. . . . 5
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16 | 15 | exbii 1718 |
. . . 4
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17 | 7, 12, 16 | 3bitr4i 281 |
. . 3
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18 | 1, 3, 17 | 3bitr4ri 282 |
. 2
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19 | 18 | eqriv 2448 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-br 4403 df-opab 4462 df-xp 4840 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 |
This theorem is referenced by: fvco2 5940 supp0cosupp0 6954 imacosupp 6955 fipreima 7880 fsuppcolem 7914 psgnunilem1 17134 gsumzf1o 17546 dprdf1o 17665 frlmup3 19358 f1lindf 19380 lindfmm 19385 cnco 20282 cnpco 20283 ptrescn 20654 xkoco1cn 20672 xkoco2cn 20673 xkococnlem 20674 qtopcn 20729 fmco 20976 uniioombllem3 22543 cncombf 22614 deg1val 23045 ofpreima 28268 mbfmco 29086 eulerpartlemmf 29208 erdsze2lem2 29927 cvmliftmolem1 30004 cvmlift2lem9a 30026 cvmlift2lem9 30034 mclsppslem 30221 poimirlem15 31955 poimirlem16 31956 poimirlem19 31959 cnambfre 31989 ftc1anclem3 32019 trclimalb2 36318 brtrclfv2 36319 frege97d 36344 frege109d 36349 frege131d 36356 extoimad 36607 imo72b2lem0 36608 imo72b2lem2 36610 imo72b2lem1 36614 imo72b2 36619 limccog 37700 |
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