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Mirrors > Home > ILE Home > Th. List > ffvelcdmi | Unicode version |
Description: A function's value belongs to its codomain. (Contributed by NM, 6-Apr-2005.) |
Ref | Expression |
---|---|
ffvelcdmi.1 |
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Ref | Expression |
---|---|
ffvelcdmi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffvelcdmi.1 |
. 2
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2 | ffvelcdm 5645 |
. 2
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3 | 1, 2 | mpan 424 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-iota 5174 df-fun 5214 df-fn 5215 df-f 5216 df-fv 5220 |
This theorem is referenced by: omgadd 10763 cjcl 10838 climmpt 11289 cn1lem 11303 climcn1lem 11308 fsumrelem 11460 efcl 11653 sincl 11695 coscl 11696 algcvg 12028 algcvgb 12030 algcvga 12031 algfx 12032 eucalgcvga 12038 eucalg 12039 sqpweven 12155 2sqpwodd 12156 ennnfonelemnn0 12403 relogcl 13943 nninfomnilem 14416 |
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