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Mirrors > Home > ILE Home > Th. List > dffun5r | Unicode version |
Description: A way of proving a relation is a function, analogous to mo2r 2051. (Contributed by Jim Kingdon, 27-May-2020.) |
Ref | Expression |
---|---|
dffun5r |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . . . . . 6 | |
2 | 1 | mo2r 2051 | . . . . 5 |
3 | opeq2 3706 | . . . . . . 7 | |
4 | 3 | eleq1d 2208 | . . . . . 6 |
5 | 4 | mo4 2060 | . . . . 5 |
6 | 2, 5 | sylib 121 | . . . 4 |
7 | 6 | alimi 1431 | . . 3 |
8 | 7 | anim2i 339 | . 2 |
9 | dffun4 5134 | . 2 | |
10 | 8, 9 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wex 1468 wcel 1480 wmo 2000 cop 3530 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-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-cnv 4547 df-co 4548 df-fun 5125 |
This theorem is referenced by: (None) |
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