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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 5032 |
. . . 4
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2 | dffn4 5252 |
. . . . 5
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3 | 2 | anbi1i 447 |
. . . 4
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4 | 1, 3 | bitri 183 |
. . 3
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5 | f11o.1 |
. . . . 5
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6 | 5 | rnex 4713 |
. . . 4
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7 | foeq3 5244 |
. . . . 5
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8 | sseq1 3048 |
. . . . 5
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9 | 7, 8 | anbi12d 458 |
. . . 4
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10 | 6, 9 | spcev 2714 |
. . 3
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11 | 4, 10 | sylbi 120 |
. 2
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12 | fof 5246 |
. . . 4
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13 | fss 5185 |
. . . 4
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14 | 12, 13 | sylan 278 |
. . 3
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15 | 14 | exlimiv 1535 |
. 2
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16 | 11, 15 | impbii 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 ax-un 4269 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-cnv 4460 df-dm 4462 df-rn 4463 df-f 5032 df-fo 5034 |
This theorem is referenced by: f11o 5299 |
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