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Mirrors > Home > ILE Home > Th. List > fvex | Unicode version |
Description: Evaluating a set function at a set exists. (Contributed by Mario Carneiro and Jim Kingdon, 28-May-2019.) |
Ref | Expression |
---|---|
fvex.1 | |
fvex.2 |
Ref | Expression |
---|---|
fvex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvex.1 | . 2 | |
2 | fvex.2 | . 2 | |
3 | fvexg 5408 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 cvv 2660 cfv 5093 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-cnv 4517 df-dm 4519 df-rn 4520 df-iota 5058 df-fv 5101 |
This theorem is referenced by: rdgtfr 6239 rdgruledefgg 6240 mapsnf1o2 6558 ixpiinm 6586 mapsnen 6673 xpdom2 6693 mapxpen 6710 xpmapenlem 6711 phplem4 6717 ac6sfi 6760 fiintim 6785 acfun 7031 ccfunen 7047 ioof 9722 frec2uzrand 10146 frec2uzf1od 10147 frecfzennn 10167 hashinfom 10492 fsum3 11124 slotslfn 11912 |
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