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Metamath Proof Explorer

Theorem strov2rcl

Description: Partial reverse closure for any structure defined as a two-argument function. (Contributed by Stefan O'Rear, 27-Mar-2015) (Proof shortened by AV, 2-Dec-2019)

	Ref	Expression
Hypotheses	strov2rcl.s	$⊢ S = I F R$
	strov2rcl.b	$⊢ B = {Base}_{S}$
	strov2rcl.f	$⊢ Rel dom F$
Assertion	strov2rcl	$⊢ X \in B \to I \in V$

Proof

Step	Hyp	Ref	Expression
1		strov2rcl.s	$⊢ S = I F R$
2		strov2rcl.b	$⊢ B = {Base}_{S}$
3		strov2rcl.f	$⊢ Rel dom F$
4	3 1 2	elbasov	$⊢ X \in B \to (I \in V \land R \in V)$
5	4	simpld	$⊢ X \in B \to I \in V$