This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem predeq3

Description: Equality theorem for the predecessor class. (Contributed by Scott Fenton, 2-Feb-2011)

		Ref	Expression
	Assertion	predeq3	$⊢ X = Y \to Pred (R, A, X) = Pred (R, A, Y)$

Step	Hyp	Ref	Expression
1		eqid	$⊢ R = R$
2		eqid	$⊢ A = A$
3		predeq123	$⊢ (R = R \land A = A \land X = Y) \to Pred (R, A, X) = Pred (R, A, Y)$
4	1 2 3	mp3an12	$⊢ X = Y \to Pred (R, A, X) = Pred (R, A, Y)$