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Mirrors > Home > ILE Home > Th. List > dff1o6 | Unicode version |
Description: A one-to-one onto function in terms of function values. (Contributed by NM, 29-Mar-2008.) |
Ref | Expression |
---|---|
dff1o6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o 5130 | . 2 | |
2 | dff13 5669 | . . 3 | |
3 | df-fo 5129 | . . 3 | |
4 | 2, 3 | anbi12i 455 | . 2 |
5 | df-3an 964 | . . 3 | |
6 | eqimss 3151 | . . . . . . 7 | |
7 | 6 | anim2i 339 | . . . . . 6 |
8 | df-f 5127 | . . . . . 6 | |
9 | 7, 8 | sylibr 133 | . . . . 5 |
10 | 9 | pm4.71ri 389 | . . . 4 |
11 | 10 | anbi1i 453 | . . 3 |
12 | an32 551 | . . 3 | |
13 | 5, 11, 12 | 3bitrri 206 | . 2 |
14 | 1, 4, 13 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wceq 1331 wral 2416 wss 3071 crn 4540 wfn 5118 wf 5119 wf1 5120 wfo 5121 wf1o 5122 cfv 5123 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 |
This theorem is referenced by: ennnfonelemim 11937 |
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