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Mirrors > Home > ILE Home > Th. List > dff1o5 | Unicode version |
Description: Alternate definition of one-to-one onto function. (Contributed by NM, 10-Dec-2003.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
dff1o5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o 4929 | . 2 | |
2 | f1f 5112 | . . . . 5 | |
3 | 2 | biantrurd 299 | . . . 4 |
4 | dffo2 5130 | . . . 4 | |
5 | 3, 4 | syl6rbbr 197 | . . 3 |
6 | 5 | pm5.32i 441 | . 2 |
7 | 1, 6 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wceq 1284 crn 4364 wf 4918 wf1 4919 wfo 4920 wf1o 4921 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 |
This theorem is referenced by: f1orescnv 5162 frec2uzf1od 9408 |
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