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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 |
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Ref | Expression |
---|---|
ffvelrni |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffvrni.1 |
. 2
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2 | ffvelrn 5561 |
. 2
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3 | 1, 2 | mpan 421 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-fv 5139 |
This theorem is referenced by: omgadd 10580 cjcl 10652 climmpt 11101 cn1lem 11115 climcn1lem 11120 fsumrelem 11272 efcl 11407 sincl 11449 coscl 11450 algcvg 11765 algcvgb 11767 algcvga 11768 algfx 11769 eucalgcvga 11775 eucalg 11776 sqpweven 11889 2sqpwodd 11890 ennnfonelemnn0 11971 relogcl 12991 nninfomnilem 13389 |
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