  We prove an a priori bound for solutions of the dynamic $\Phi^4_3$ equation.
This bound provides a control on solutions on a compact space-time set only in
terms of the realisation of the noise on an enlargement of this set, and it
does not depend on any choice of space-time boundary conditions.
  We treat the large and small scale behaviour of solutions with completely
different arguments. For small scales we use bounds akin to those presented in
Hairer's theory of regularity structures. We stress immediately that our proof
is fully self-contained, but we give a detailed explanation of how our
arguments relate to Hairer's. For large scales we use a PDE argument based on
the maximum principle. Both regimes are connected by a solution-dependent
regularisation procedure.
  The fact that our bounds do not depend on space-time boundary conditions
makes them useful for the analysis of large scale properties of solutions. They
can for example be used in a compactness argument to construct solutions on the
full space and their invariant measures.
