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Mirrors > Home > ILE Home > Th. List > dff1o3 | Unicode version |
Description: Alternate definition of one-to-one onto function. (Contributed by NM, 25-Mar-1998.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
dff1o3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anan32 984 | . 2 | |
2 | dff1o2 5445 | . 2 | |
3 | df-fo 5202 | . . 3 | |
4 | 3 | anbi1i 455 | . 2 |
5 | 1, 2, 4 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 973 wceq 1348 ccnv 4608 crn 4610 wfun 5190 wfn 5191 wfo 5194 wf1o 5195 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-in 3127 df-ss 3134 df-f 5200 df-f1 5201 df-fo 5202 df-f1o 5203 |
This theorem is referenced by: f1ofo 5447 resdif 5462 f11o 5473 f1opw 6053 1stconst 6197 2ndconst 6198 f1o2ndf1 6204 ssdomg 6752 phplem4 6829 phplem4on 6841 |
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