MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-evpm Structured version   Visualization version   GIF version

Definition df-evpm 18118
Description: Define the set of even permutations on a given set. (Contributed by Stefan O'Rear, 9-Jul-2018.)
Assertion
Ref Expression
df-evpm pmEven = (𝑑 ∈ V ↦ ((pmSgn‘𝑑) “ {1}))

Detailed syntax breakdown of Definition df-evpm
StepHypRef Expression
1 cevpm 18116 . 2 class pmEven
2 vd . . 3 setvar 𝑑
3 cvv 3349 . . 3 class V
42cv 1629 . . . . . 6 class 𝑑
5 cpsgn 18115 . . . . . 6 class pmSgn
64, 5cfv 6031 . . . . 5 class (pmSgn‘𝑑)
76ccnv 5248 . . . 4 class (pmSgn‘𝑑)
8 c1 10138 . . . . 5 class 1
98csn 4314 . . . 4 class {1}
107, 9cima 5252 . . 3 class ((pmSgn‘𝑑) “ {1})
112, 3, 10cmpt 4861 . 2 class (𝑑 ∈ V ↦ ((pmSgn‘𝑑) “ {1}))
121, 11wceq 1630 1 wff pmEven = (𝑑 ∈ V ↦ ((pmSgn‘𝑑) “ {1}))
Colors of variables: wff setvar class
This definition is referenced by:  evpmss  20146  psgnevpmb  20147
  Copyright terms: Public domain W3C validator