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Mirrors > Home > ILE Home > Th. List > dff1o2 | Unicode version |
Description: Alternate definition of one-to-one onto function. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
dff1o2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o 4909 | . 2 | |
2 | df-f1 4907 | . . . 4 | |
3 | df-fo 4908 | . . . 4 | |
4 | 2, 3 | anbi12i 433 | . . 3 |
5 | anass 381 | . . . 4 | |
6 | 3anan12 897 | . . . . . 6 | |
7 | 6 | anbi1i 431 | . . . . 5 |
8 | eqimss 2997 | . . . . . . . 8 | |
9 | df-f 4906 | . . . . . . . . 9 | |
10 | 9 | biimpri 124 | . . . . . . . 8 |
11 | 8, 10 | sylan2 270 | . . . . . . 7 |
12 | 11 | 3adant2 923 | . . . . . 6 |
13 | 12 | pm4.71i 371 | . . . . 5 |
14 | ancom 253 | . . . . 5 | |
15 | 7, 13, 14 | 3bitr4ri 202 | . . . 4 |
16 | 5, 15 | bitri 173 | . . 3 |
17 | 4, 16 | bitri 173 | . 2 |
18 | 1, 17 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 w3a 885 wceq 1243 wss 2917 ccnv 4344 crn 4346 wfun 4896 wfn 4897 wf 4898 wf1 4899 wfo 4900 wf1o 4901 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-in 2924 df-ss 2931 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 |
This theorem is referenced by: dff1o3 5132 dff1o4 5134 f1orn 5136 dif1en 6337 |
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