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

Metamath Proof Explorer

Theorem ssralvOLD

Description: Obsolete version of ssralv as of 19-May-2025. (Contributed by NM, 11-Mar-2006) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	ssralvOLD	$⊢ A \subseteq B \to (\forall x \in B φ \to \forall x \in A φ)$

Proof

Step	Hyp	Ref	Expression
1		ssel	$⊢ A \subseteq B \to (x \in A \to x \in B)$
2	1	imim1d	$⊢ A \subseteq B \to ((x \in B \to φ) \to (x \in A \to φ))$
3	2	ralimdv2	$⊢ A \subseteq B \to (\forall x \in B φ \to \forall x \in A φ)$