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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 5189 | . 2 | |
2 | df-f1 5187 | . . . 4 | |
3 | df-fo 5188 | . . . 4 | |
4 | 2, 3 | anbi12i 456 | . . 3 |
5 | anass 399 | . . . 4 | |
6 | 3anan12 979 | . . . . . 6 | |
7 | 6 | anbi1i 454 | . . . . 5 |
8 | eqimss 3191 | . . . . . . . 8 | |
9 | df-f 5186 | . . . . . . . . 9 | |
10 | 9 | biimpri 132 | . . . . . . . 8 |
11 | 8, 10 | sylan2 284 | . . . . . . 7 |
12 | 11 | 3adant2 1005 | . . . . . 6 |
13 | 12 | pm4.71i 389 | . . . . 5 |
14 | ancom 264 | . . . . 5 | |
15 | 7, 13, 14 | 3bitr4ri 212 | . . . 4 |
16 | 5, 15 | bitri 183 | . . 3 |
17 | 4, 16 | bitri 183 | . 2 |
18 | 1, 17 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 967 wceq 1342 wss 3111 ccnv 4597 crn 4599 wfun 5176 wfn 5177 wf 5178 wf1 5179 wfo 5180 wf1o 5181 |
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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3117 df-ss 3124 df-f 5186 df-f1 5187 df-fo 5188 df-f1o 5189 |
This theorem is referenced by: dff1o3 5432 dff1o4 5434 f1orn 5436 dif1en 6836 fiintim 6885 |
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