Theorem elpredim

Description: Membership in a predecessor class - implicative version. (Contributed by Scott Fenton, 9-May-2012) (Proof shortened by BJ, 16-Oct-2024)

	Ref	Expression
Hypothesis	elpredim.1	|- X e. _V
Assertion	elpredim	|- ( Y e. Pred ( R , A , X ) -> Y R X )

Proof

Step	Hyp	Ref	Expression
1		elpredim.1	|- X e. _V
2		elpredimg	|- ( ( X e. _V /\ Y e. Pred ( R , A , X ) ) -> Y R X )
3	1 2	mpan	|- ( Y e. Pred ( R , A , X ) -> Y R X )