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Metamath Proof Explorer

Theorem lmodbn0

Description: The base set of a left module is nonempty. (Contributed by NM, 8-Dec-2013) (Revised by Mario Carneiro, 19-Jun-2014)

		Ref	Expression
	Hypothesis	lmodbn0.b	$⊢ B = {Base}_{W}$
	Assertion	lmodbn0	$⊢ W \in LMod \to B \neq \emptyset$

Step	Hyp	Ref	Expression
1		lmodbn0.b	$⊢ B = {Base}_{W}$
2		lmodgrp	$⊢ W \in LMod \to W \in Grp$
3	1	grpbn0	$⊢ W \in Grp \to B \neq \emptyset$
4	2 3	syl	$⊢ W \in LMod \to B \neq \emptyset$