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Mirrors > Home > ILE Home > Th. List > dffn2 | Unicode version |
Description: Any function is a mapping into . (Contributed by NM, 31-Oct-1995.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) |
Ref | Expression |
---|---|
dffn2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssv 3150 | . . 3 | |
2 | 1 | biantru 300 | . 2 |
3 | df-f 5176 | . 2 | |
4 | 2, 3 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 cvv 2712 wss 3102 crn 4589 wfn 5167 wf 5168 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 df-in 3108 df-ss 3115 df-f 5176 |
This theorem is referenced by: f1cnvcnv 5388 fcoconst 5640 fnressn 5655 1stcof 6113 2ndcof 6114 fnmpo 6152 tposfn 6222 tfrlemibfn 6277 tfr1onlembfn 6293 mptelixpg 6681 |
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