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Theorem fconstmpt 4415
 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.)
Assertion
Ref Expression
fconstmpt
Distinct variable groups:   ,   ,

Proof of Theorem fconstmpt
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 velsn 3420 . . . 4
21anbi2i 438 . . 3
32opabbii 3852 . 2
4 df-xp 4379 . 2
5 df-mpt 3848 . 2
63, 4, 53eqtr4i 2086 1
 Colors of variables: wff set class Syntax hints:   wa 101   wceq 1259   wcel 1409  csn 3403  copab 3845   cmpt 3846   cxp 4371 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-sn 3409  df-opab 3847  df-mpt 3848  df-xp 4379 This theorem is referenced by:  fconst  5110  fcoconst  5362  fmptsn  5380  ofc12  5759  caofinvl  5761  xpexgALT  5788
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