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Mirrors > Home > ILE Home > Th. List > imaco | 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 2461 |
. . 3
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2 | vex 2740 |
. . . 4
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3 | 2 | elima 4975 |
. . 3
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4 | rexcom4 2760 |
. . . . 5
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5 | r19.41v 2633 |
. . . . . 6
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6 | 5 | exbii 1605 |
. . . . 5
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7 | 4, 6 | bitri 184 |
. . . 4
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8 | 2 | elima 4975 |
. . . . 5
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9 | vex 2740 |
. . . . . . 7
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10 | 9, 2 | brco 4798 |
. . . . . 6
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11 | 10 | rexbii 2484 |
. . . . 5
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12 | 8, 11 | bitri 184 |
. . . 4
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13 | vex 2740 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
14 | 13 | elima 4975 |
. . . . . 6
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15 | 14 | anbi1i 458 |
. . . . 5
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16 | 15 | exbii 1605 |
. . . 4
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17 | 7, 12, 16 | 3bitr4i 212 |
. . 3
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18 | 1, 3, 17 | 3bitr4ri 213 |
. 2
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19 | 18 | eqriv 2174 |
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 4121 ax-pow 4174 ax-pr 4209 |
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 3577 df-sn 3598 df-pr 3599 df-op 3601 df-br 4004 df-opab 4065 df-xp 4632 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 |
This theorem is referenced by: fvco2 5585 cnco 13614 cnptopco 13615 |
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