Edit (old answer was really complicated without such need)
Second way without \ontop command:
\documentclass{article}
\usepackage{adjustbox}
\usepackage{tabularx}
\usepackage{amsmath}
\begin{document}
\textbf{Condition}:
$\begin{aligned}[t]
(\exists a \in A) (\exists b \in B)(\forall c \in C)[&F(a,b)=c~\wedge~F(c,d)=a~\wedge~ \\
&a \in X~\wedge~(c \in Y ~\vee~d \in M)]
\end{aligned}$
\end{document}
Same output as below with no extra space.
Old Answer:
The problem is that inline math are supposed to centered vertical with the text. What you want is a top aligned tabular.
So, you can try like this:
\documentclass{article}
\usepackage{amsmath}
\def\ontop#1{\vtop{\null\hbox{#1}}}
\begin{document}
\begin{tabular}{cc}\ontop{\textbf{Condition}:}&\ontop{$\begin{aligned}
(\exists a \in A) (\exists b \in B)(\forall c \in C)[&F(a,b)=c~\wedge~F(c,d)=a~\wedge~ \\
&a \in X~\wedge~(c \in Y ~\vee~d \in M)]
\end{aligned}$}\end{tabular}
\end{document}
Source of \ontop command from here:
https://tex.stackexchange.com/a/23522/120578
Output:

\aligned[t]does also work with any kind of math, don't you think? – Oct 16 '17 at 00:57-1?! – Oct 16 '17 at 00:59\dfracand you want to align with its top part... Check it to see it is different result with the second option. I just left it there because may be found useful in other cases. – koleygr Oct 16 '17 at 01:05aligned[t]even works in the case of\dfrac. – Oct 16 '17 at 01:07