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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 |
Ref | Expression |
---|---|
ffoss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f 5200 | . . . 4 | |
2 | dffn4 5424 | . . . . 5 | |
3 | 2 | anbi1i 455 | . . . 4 |
4 | 1, 3 | bitri 183 | . . 3 |
5 | f11o.1 | . . . . 5 | |
6 | 5 | rnex 4876 | . . . 4 |
7 | foeq3 5416 | . . . . 5 | |
8 | sseq1 3170 | . . . . 5 | |
9 | 7, 8 | anbi12d 470 | . . . 4 |
10 | 6, 9 | spcev 2825 | . . 3 |
11 | 4, 10 | sylbi 120 | . 2 |
12 | fof 5418 | . . . 4 | |
13 | fss 5357 | . . . 4 | |
14 | 12, 13 | sylan 281 | . . 3 |
15 | 14 | exlimiv 1591 | . 2 |
16 | 11, 15 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1348 wex 1485 wcel 2141 cvv 2730 wss 3121 crn 4610 wfn 5191 wf 5192 wfo 5194 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 ax-un 4416 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-cnv 4617 df-dm 4619 df-rn 4620 df-f 5200 df-fo 5202 |
This theorem is referenced by: f11o 5473 |
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