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Theorem mptv 5718
 Description: Function with universal domain in maps-to notation. (Contributed by set.mm contributors, 16-Aug-2013.)
Assertion
Ref Expression
mptv (x V B) = {x, y y = B}
Distinct variable groups:   x,y   y,B
Allowed substitution hint:   B(x)

Proof of Theorem mptv
StepHypRef Expression
1 df-mpt 5652 . 2 (x V B) = {x, y (x V y = B)}
2 vex 2862 . . . 4 x V
32biantrur 492 . . 3 (y = B ↔ (x V y = B))
43opabbii 4626 . 2 {x, y y = B} = {x, y (x V y = B)}
51, 4eqtr4i 2376 1 (x V B) = {x, y y = B}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  Vcvv 2859  {copab 4622   ↦ cmpt 5651 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-v 2861  df-opab 4623  df-mpt 5652 This theorem is referenced by:  csucex  6259  brcsuc  6260  frecsuc  6322
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