My professor of Algebra use some "strange" notation for me. He uses $\bigvee$ instead $\exists$ and $\bigwedge$ instead $\forall$. For example $$\displaystyle\bigwedge_{x\in \mathbb{Z}}\bigwedge_{m\in \mathbb{Z}\backslash\{0\}}\bigvee_{q,r\in \mathbb{Z}}(x=qm+r \wedge 0\leq r<|m|)$$ is same as $(\forall x \in \mathbb{Z})(\forall m \in \mathbb{Z}\backslash \{0\}) (\exists q,r \in \mathbb{Z}) (x=qm+r \wedge 0\leq r<|m|) $. If we know the set with which we are working, then we say $\displaystyle\bigwedge_{x}\bigvee_{y}(x+y=0)$ (without saying $x \in \text{Set}$). I asked him for this notation, and he said that I can see this in
K.Kuratowski, A.Mostowski, Set theory, PWN, Warszawa, 1976.
I found this book in library and it's really true.
Could someone say something more about this notation? Is this standard notation in mathematics? Did you see it anywhere else?