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Theorem fconstmpt 5681
 Description: Representation of a constant function using the mapping operation. (Note that x cannot appear free in B.) (Contributed by set.mm contributors, 16-Nov-2013.)
Assertion
Ref Expression
fconstmpt (A × {B}) = (x A B)
Distinct variable groups:   x,A   x,B

Proof of Theorem fconstmpt
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 fconstopab 4815 . 2 (A × {B}) = {x, y (x A y = B)}
2 df-mpt 5652 . 2 (x A B) = {x, y (x A y = B)}
31, 2eqtr4i 2376 1 (A × {B}) = (x A B)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  {csn 3737  {copab 4622   × cxp 4770   ↦ cmpt 5651 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sn 3741  df-opab 4623  df-xp 4784  df-mpt 5652 This theorem is referenced by: (None)
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