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Mirrors > Home > ILE Home > Th. List > funfni | Unicode version |
Description: Inference to convert a function and domain antecedent. (Contributed by NM, 22-Apr-2004.) |
Ref | Expression |
---|---|
funfni.1 |
Ref | Expression |
---|---|
funfni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnfun 5190 | . . 3 | |
2 | 1 | adantr 274 | . 2 |
3 | fndm 5192 | . . . 4 | |
4 | 3 | eleq2d 2187 | . . 3 |
5 | 4 | biimpar 295 | . 2 |
6 | funfni.1 | . 2 | |
7 | 2, 5, 6 | syl2anc 408 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1465 cdm 4509 wfun 5087 wfn 5088 |
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-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 df-fn 5096 |
This theorem is referenced by: fneu 5197 fnbrfvb 5430 fvelrnb 5437 fvelimab 5445 fniinfv 5447 fvco2 5458 eqfnfv 5486 fndmdif 5493 fndmin 5495 elpreima 5507 fniniseg 5508 fniniseg2 5510 fnniniseg2 5511 rexsupp 5512 fnopfv 5518 fnfvelrn 5520 rexrn 5525 ralrn 5526 fsn2 5562 fnressn 5574 eufnfv 5616 rexima 5624 ralima 5625 fniunfv 5631 dff13 5637 foeqcnvco 5659 f1eqcocnv 5660 isocnv2 5681 isoini 5687 f1oiso 5695 fnovex 5772 suppssof1 5967 offveqb 5969 1stexg 6033 2ndexg 6034 smoiso 6167 rdgruledefgg 6240 rdgivallem 6246 frectfr 6265 frecrdg 6273 en1 6661 fnfi 6793 ordiso2 6888 slotex 11913 |
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