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Mirrors > Home > ILE Home > Th. List > funmo | Unicode version |
Description: A function has at most one value for each argument. (Contributed by NM, 24-May-1998.) |
Ref | Expression |
---|---|
funmo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun6 5137 | . . . . . 6 | |
2 | 1 | simplbi 272 | . . . . 5 |
3 | brrelex 4579 | . . . . . 6 | |
4 | 3 | ex 114 | . . . . 5 |
5 | 2, 4 | syl 14 | . . . 4 |
6 | 5 | ancrd 324 | . . 3 |
7 | 6 | alrimiv 1846 | . 2 |
8 | breq1 3932 | . . . . . . 7 | |
9 | 8 | mobidv 2035 | . . . . . 6 |
10 | 9 | imbi2d 229 | . . . . 5 |
11 | 1 | simprbi 273 | . . . . . 6 |
12 | 11 | 19.21bi 1537 | . . . . 5 |
13 | 10, 12 | vtoclg 2746 | . . . 4 |
14 | 13 | com12 30 | . . 3 |
15 | moanimv 2074 | . . 3 | |
16 | 14, 15 | sylibr 133 | . 2 |
17 | moim 2063 | . 2 | |
18 | 7, 16, 17 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wceq 1331 wcel 1480 wmo 2000 cvv 2686 class class class wbr 3929 wrel 4544 wfun 5117 |
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-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-fun 5125 |
This theorem is referenced by: funeu 5148 funco 5163 imadif 5203 fneu 5227 dff3im 5565 shftfn 10596 |
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