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Mirrors > Home > ILE Home > Th. List > funfveu | Unicode version |
Description: A function has one value given an argument in its domain. (Contributed by Jim Kingdon, 29-Dec-2018.) |
Ref | Expression |
---|---|
funfveu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2233 | . . . . 5 | |
2 | 1 | anbi2d 461 | . . . 4 |
3 | breq1 3992 | . . . . 5 | |
4 | 3 | eubidv 2027 | . . . 4 |
5 | 2, 4 | imbi12d 233 | . . 3 |
6 | dffun8 5226 | . . . . 5 | |
7 | 6 | simprbi 273 | . . . 4 |
8 | 7 | r19.21bi 2558 | . . 3 |
9 | 5, 8 | vtoclg 2790 | . 2 |
10 | 9 | anabsi7 576 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 weu 2019 wcel 2141 wral 2448 class class class wbr 3989 cdm 4611 wrel 4616 wfun 5192 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-id 4278 df-cnv 4619 df-co 4620 df-dm 4621 df-fun 5200 |
This theorem is referenced by: funfvex 5513 |
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