Definition df-wsuc 31756

Description: Define the concept of a successor in a well-founded set. (Contributed by Scott Fenton, 13-Jun-2018.) (Revised by AV, 10-Oct-2021.)

Assertion

Ref	Expression
df-wsuc	|- wsuc ( R , A , X ) = inf ( Pred ( `' R , A , X ) , A , R )

Detailed syntax breakdown of Definition df-wsuc

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cR	. . 3 class R
3		cX	. . 3 class X
4	1, 2, 3	cwsuc 31752	. 2 class wsuc ( R , A , X )
5	2	ccnv 5113	. . . 4 class `' R
6	1, 5, 3	cpred 5679	. . 3 class Pred ( `' R , A , X )
7	6, 1, 2	cinf 8347	. 2 class inf ( Pred ( `' R , A , X ) , A , R )
8	4, 7	wceq 1483	1 wff wsuc ( R , A , X ) = inf ( Pred ( `' R , A , X ) , A , R )

This definition is referenced by:  wsuceq123  31760  nfwsuc  31764  wsucex  31775  wsuccl  31776  wsuclb  31777