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Mirrors > Home > ILE Home > Th. List > fconstmpt | Unicode version |
Description: Representation of a constant function using the mapping operation. (Note that cannot appear free in .) (Contributed by NM, 12-Oct-1999.) (Revised by Mario Carneiro, 16-Nov-2013.) |
Ref | Expression |
---|---|
fconstmpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | velsn 3539 | . . . 4 | |
2 | 1 | anbi2i 452 | . . 3 |
3 | 2 | opabbii 3990 | . 2 |
4 | df-xp 4540 | . 2 | |
5 | df-mpt 3986 | . 2 | |
6 | 3, 4, 5 | 3eqtr4i 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wcel 1480 csn 3522 copab 3983 cmpt 3984 cxp 4532 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sn 3528 df-opab 3985 df-mpt 3986 df-xp 4540 |
This theorem is referenced by: fconst 5313 fcoconst 5584 fmptsn 5602 fconstmpo 5859 ofc12 5995 caofinvl 5997 xpexgALT 6024 inftonninf 10207 fser0const 10282 cnmptc 12440 dvexp 12833 dvexp2 12834 dvmptidcn 12836 dvmptccn 12837 dvef 12845 nninfall 13193 nninfsellemeqinf 13201 nninffeq 13205 exmidsbthrlem 13206 |
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