Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2220 | . . . . 5 | |
2 | 1 | anbi2d 460 | . . . 4 |
3 | breq1 3970 | . . . . 5 | |
4 | 3 | eubidv 2014 | . . . 4 |
5 | 2, 4 | imbi12d 233 | . . 3 |
6 | dffun8 5200 | . . . . 5 | |
7 | 6 | simprbi 273 | . . . 4 |
8 | 7 | r19.21bi 2545 | . . 3 |
9 | 5, 8 | vtoclg 2772 | . 2 |
10 | 9 | anabsi7 571 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 weu 2006 wcel 2128 wral 2435 class class class wbr 3967 cdm 4588 wrel 4593 wfun 5166 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-br 3968 df-opab 4028 df-id 4255 df-cnv 4596 df-co 4597 df-dm 4598 df-fun 5174 |
This theorem is referenced by: funfvex 5487 |
Copyright terms: Public domain | W3C validator |