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

Metamath Proof Explorer

Theorem bnj213

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Assertion	bnj213	$⊢ pred (X, A, R) \subseteq A$

Step	Hyp	Ref	Expression
1		df-bnj14	$⊢ pred (X, A, R) = \{y \in A \| y R X\}$
2	1	ssrab3	$⊢ pred (X, A, R) \subseteq A$