Definition df-wsuc 36310

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 36308	. 2 class wsuc(𝑅, 𝐴, 𝑋)
5	2	ccnv 5660	. . . 4 class ◡𝑅
6	1, 5, 3	cpred 6301	. . 3 class Pred(◡𝑅, 𝐴, 𝑋)
7	6, 1, 2	cinf 9397	. 2 class inf(Pred(◡𝑅, 𝐴, 𝑋), 𝐴, 𝑅)
8	4, 7	wceq 1570	1 wff wsuc(𝑅, 𝐴, 𝑋) = inf(Pred(◡𝑅, 𝐴, 𝑋), 𝐴, 𝑅)

This definition is used by:  wsuceq123  36312  nfwsuc  36316  wsucex  36324  wsuccl  36325  wsuclb  36326