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Metamath Proof Explorer

Theorem bnj1418

Description: Property of _pred . (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Assertion	bnj1418	$⊢ y \in pred (x, A, R) \to y R x$

Step	Hyp	Ref	Expression
1		breq1	$⊢ z = y \to (z R x \leftrightarrow y R x)$
2		df-bnj14	$⊢ pred (x, A, R) = \{z \in A \| z R x\}$
3	2	bnj1538	$⊢ z \in pred (x, A, R) \to z R x$
4	1 3	vtoclga	$⊢ y \in pred (x, A, R) \to y R x$