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Mirrors > Home > ILE Home > Th. List > ffvelrni | Unicode version |
Description: A function's value belongs to its codomain. (Contributed by NM, 6-Apr-2005.) |
Ref | Expression |
---|---|
ffvrni.1 |
Ref | Expression |
---|---|
ffvelrni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffvrni.1 | . 2 | |
2 | ffvelrn 5553 | . 2 | |
3 | 1, 2 | mpan 420 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 wf 5119 cfv 5123 |
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-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-fv 5131 |
This theorem is referenced by: omgadd 10548 cjcl 10620 climmpt 11069 cn1lem 11083 climcn1lem 11088 fsumrelem 11240 efcl 11370 sincl 11413 coscl 11414 algcvg 11729 algcvgb 11731 algcvga 11732 algfx 11733 eucalgcvga 11739 eucalg 11740 sqpweven 11853 2sqpwodd 11854 ennnfonelemnn0 11935 nninfomnilem 13214 |
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