Theorem wrd0

Description: The empty set is a word (theempty word, frequently denoted ε in this context). This corresponds to the definition in Section 9.1 of AhoHopUll p. 318. (Contributed by Stefan O'Rear, 15-Aug-2015) (Proof shortened by AV, 13-May-2020)

	Ref	Expression
Assertion	wrd0	$$⊢\varnothing \in \mathrm{Word}S$$

Proof

Step	Hyp	Ref	Expression
1		f0	$$⊢\varnothing :\varnothing ⟶S$$
2		iswrddm0	$$⊢\varnothing :\varnothing ⟶S\to \varnothing \in \mathrm{Word}S$$
3	1 2	ax-mp	$$⊢\varnothing \in \mathrm{Word}S$$