\newcommand{\py}{\pay{P}}
\newcommand{\pn}{\pan{P}}
+\newcommand{\pc}{\pa{C}}
+\newcommand{\pcy}{\pay{C}}
+\newcommand{\pcn}{\pan{C}}
+
\newcommand{\pl}{\pa{L}}
\newcommand{\ply}{\pay{L}}
\newcommand{\pln}{\pan{L}}
{\hbox{\normalsize$\forall$}}%
{\hbox{\scriptsize$\forall$}}}%
}
+\newcommand{\bigexists}{%
+ \mathop{\mathchoice%
+ {\hbox{\huge$\exists$}}%
+ {\hbox{\Large$\exists$}}%
+ {\hbox{\normalsize$\exists$}}%
+ {\hbox{\scriptsize$\exists$}}}%
+}
\newcommand{\Largeexists}{\mathop{\hbox{\Large$\exists$}}}
\newcommand{\Largenexists}{\mathop{\hbox{\Large$\nexists$}}}