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Mirrors > Home > ILE Home > Th. List > fnmpt | Unicode version |
Description: The maps-to notation defines a function with domain. (Contributed by NM, 9-Apr-2013.) |
Ref | Expression |
---|---|
mptfng.1 |
Ref | Expression |
---|---|
fnmpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2697 | . . 3 | |
2 | 1 | ralimi 2495 | . 2 |
3 | mptfng.1 | . . 3 | |
4 | 3 | mptfng 5248 | . 2 |
5 | 2, 4 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 wral 2416 cvv 2686 cmpt 3989 wfn 5118 |
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-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-fun 5125 df-fn 5126 |
This theorem is referenced by: mpt0 5250 ralrnmpt 5562 rexrnmpt 5563 fmpt 5570 fmpt2d 5582 f1ocnvd 5972 offval2 5997 ofrfval2 5998 caofinvl 6004 f1od2 6132 frectfr 6297 omfnex 6345 oeiv 6352 mptelixpg 6628 fifo 6868 efcvgfsum 11373 neif 12310 tgrest 12338 dvrecap 12846 nninfalllemn 13202 |
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