Definition df-evpm 19515

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

Step	Hyp	Ref	Expression
1		cevpm 19513	. 2 class pmEven
2		vd	. . 3 setvar 𝑑
3		cvv 3453	. . 3 class V
4	2	cv 1558	. . . . . 6 class 𝑑
5		cpsgn 19512	. . . . . 6 class pmSgn
6	4, 5	cfv 6517	. . . . 5 class (pmSgn‘𝑑)
7	6	ccnv 5644	. . . 4 class ◡(pmSgn‘𝑑)
8		c1 11071	. . . . 5 class 1
9	8	csn 4581	. . . 4 class {1}
10	7, 9	cima 5648	. . 3 class (◡(pmSgn‘𝑑) “ {1})
11	2, 3, 10	cmpt 5180	. 2 class (𝑑 ∈ V ↦ (◡(pmSgn‘𝑑) “ {1}))
12	1, 11	wceq 1559	1 wff pmEven = (𝑑 ∈ V ↦ (◡(pmSgn‘𝑑) “ {1}))

This definition is referenced by:  evpmss  21618  psgnevpmb  21619  evpmval  33286  altgnsg  33290