Wikipedia definition of graph homomorphism: is this correct?

Consider the definition of a graph homomorphism given here:

A graph homomorphism $f$ from a graph $G=(V,E)$ to a graph $G'=(V',E')$, written $f:G \rightarrow G'$, is a mapping $f:V \rightarrow V'$ from the vertex set of $G$ to the vertex set of $G'$ such that $\{u,v\}\in E$ implies $\{f(u),f(v)\}\in E'$.

At the beginning the article states "...a graph homomorphism is a mapping between two graphs that respects their structure. ..."

So I was wondering:

Is it a typo or is "implies" really enough?

Shouldn't it be

A graph homomorphism $f$ from a graph $G=(V,E)$ to a graph $G'=(V',E')$, written $f:G \rightarrow G'$, is a mapping $f:V \rightarrow V'$ from the vertex set of $G$ to the vertex set of $G'$ such that $\{u,v\}\in E$ if and only if $\{f(u),f(v)\}\in E'$.?