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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 ![]() ![]() |
Ref | Expression |
---|---|
fconstmpt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | velsn 3549 |
. . . 4
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2 | 1 | anbi2i 453 |
. . 3
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3 | 2 | opabbii 4003 |
. 2
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4 | df-xp 4553 |
. 2
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5 | df-mpt 3999 |
. 2
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6 | 3, 4, 5 | 3eqtr4i 2171 |
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-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-sn 3538 df-opab 3998 df-mpt 3999 df-xp 4553 |
This theorem is referenced by: fconst 5326 fcoconst 5599 fmptsn 5617 fconstmpo 5874 ofc12 6010 caofinvl 6012 xpexgALT 6039 inftonninf 10245 fser0const 10320 cnmptc 12490 dvexp 12883 dvexp2 12884 dvmptidcn 12886 dvmptccn 12887 dvef 12896 nninfall 13379 nninfsellemeqinf 13387 nninffeq 13391 exmidsbthrlem 13392 |
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