Definition df-evpm 19510

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 19508	. 2 class pmEven
2		vd	. . 3 setvar 𝑑
3		cvv 3480	. . 3 class V
4	2	cv 1539	. . . . . 6 class 𝑑
5		cpsgn 19507	. . . . . 6 class pmSgn
6	4, 5	cfv 6561	. . . . 5 class (pmSgn‘𝑑)
7	6	ccnv 5684	. . . 4 class ◡(pmSgn‘𝑑)
8		c1 11156	. . . . 5 class 1
9	8	csn 4626	. . . 4 class {1}
10	7, 9	cima 5688	. . 3 class (◡(pmSgn‘𝑑) “ {1})
11	2, 3, 10	cmpt 5225	. 2 class (𝑑 ∈ V ↦ (◡(pmSgn‘𝑑) “ {1}))
12	1, 11	wceq 1540	1 wff pmEven = (𝑑 ∈ V ↦ (◡(pmSgn‘𝑑) “ {1}))

This definition is referenced by:  evpmss  21604  psgnevpmb  21605  evpmval  33165  altgnsg  33169