Metamath Proof Explorer


Definition df-coels

Description: Define the class of coelements on the class A , see also the alternate definition dfcoels . Possible definitions are the special cases of dfcoss3 and dfcoss4 . (Contributed by Peter Mazsa, 20-Nov-2019)

Ref Expression
Assertion df-coels
|- ~ A = ,~ ( `' _E |` A )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA
 |-  A
1 0 ccoels
 |-  ~ A
2 cep
 |-  _E
3 2 ccnv
 |-  `' _E
4 3 0 cres
 |-  ( `' _E |` A )
5 4 ccoss
 |-  ,~ ( `' _E |` A )
6 1 5 wceq
 |-  ~ A = ,~ ( `' _E |` A )