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Mirrors > Home > ILE Home > Th. List > cnvresima | Unicode version |
Description: An image under the converse of a restriction. (Contributed by Jeff Hankins, 12-Jul-2009.) |
Ref | Expression |
---|---|
cnvresima |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2755 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | 1 | elima3 4995 |
. . 3
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3 | 1 | elima3 4995 |
. . . . 5
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4 | 3 | anbi1i 458 |
. . . 4
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5 | elin 3333 |
. . . 4
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6 | vex 2755 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() | |
7 | 6, 1 | opelcnv 4827 |
. . . . . . . . 9
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8 | 6 | opelres 4930 |
. . . . . . . . . 10
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9 | 6, 1 | opelcnv 4827 |
. . . . . . . . . . 11
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10 | 9 | anbi1i 458 |
. . . . . . . . . 10
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11 | 8, 10 | bitr4i 187 |
. . . . . . . . 9
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12 | 7, 11 | bitri 184 |
. . . . . . . 8
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13 | 12 | anbi2i 457 |
. . . . . . 7
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14 | anass 401 |
. . . . . . 7
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15 | 13, 14 | bitr4i 187 |
. . . . . 6
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16 | 15 | exbii 1616 |
. . . . 5
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17 | 19.41v 1914 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 16, 17 | bitri 184 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 4, 5, 18 | 3bitr4ri 213 |
. . 3
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20 | 2, 19 | bitri 184 |
. 2
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21 | 20 | eqriv 2186 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4650 df-cnv 4652 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 |
This theorem is referenced by: cnrest 14212 |
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