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Mirrors > Home > ILE Home > Th. List > ffoss | Unicode version |
Description: Relationship between a mapping and an onto mapping. Figure 38 of [Enderton] p. 145. (Contributed by NM, 10-May-1998.) |
Ref | Expression |
---|---|
f11o.1 |
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Ref | Expression |
---|---|
ffoss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f 5236 |
. . . 4
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2 | dffn4 5460 |
. . . . 5
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3 | 2 | anbi1i 458 |
. . . 4
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4 | 1, 3 | bitri 184 |
. . 3
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5 | f11o.1 |
. . . . 5
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6 | 5 | rnex 4909 |
. . . 4
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7 | foeq3 5452 |
. . . . 5
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8 | sseq1 3193 |
. . . . 5
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9 | 7, 8 | anbi12d 473 |
. . . 4
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10 | 6, 9 | spcev 2847 |
. . 3
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11 | 4, 10 | sylbi 121 |
. 2
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12 | fof 5454 |
. . . 4
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13 | fss 5393 |
. . . 4
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14 | 12, 13 | sylan 283 |
. . 3
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15 | 14 | exlimiv 1609 |
. 2
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16 | 11, 15 | impbii 126 |
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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 |
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-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-uni 3825 df-br 4019 df-opab 4080 df-cnv 4649 df-dm 4651 df-rn 4652 df-f 5236 df-fo 5238 |
This theorem is referenced by: f11o 5510 |
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