Below I want to show a property of a simple graph $G=(V,E)$ - a graph in which each edge connects two different vertices and where no two edges connect the same pair of vertices - using a compound statement that involves multiple logical variables.
When a compound statement $P(e,e^{'},v,u): \space "e=\{v,u\}\land v\neq\land e^{'}=\{v,u\}"$ is given, then $ (\forall e:e\in E)(\nexists e^{'}: e^{'} \in E)(\exists v:v\in V)(\exists v : v \in V)(P(e,e^{'},v,u)) $ is true.
Is it acceptable to express in such a provided way?