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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 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | velsn 3609 |
. . . 4
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2 | 1 | anbi2i 457 |
. . 3
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3 | 2 | opabbii 4070 |
. 2
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4 | df-xp 4632 |
. 2
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5 | df-mpt 4066 |
. 2
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6 | 3, 4, 5 | 3eqtr4i 2208 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-sn 3598 df-opab 4065 df-mpt 4066 df-xp 4632 |
This theorem is referenced by: fconst 5411 fcoconst 5687 fmptsn 5705 fconstmpo 5969 ofc12 6102 caofinvl 6104 xpexgALT 6133 inftonninf 10440 fser0const 10515 prod1dc 11593 cnmptc 13752 dvexp 14145 dvexp2 14146 dvmptidcn 14148 dvmptccn 14149 dvef 14158 nninfall 14728 nninfsellemeqinf 14735 exmidsbthrlem 14740 |
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