Contrary to the situation in May price pressure should also have eased for core inflation. The market expects 3.1% for the overall rate and 5.0% for the core rate.

Of course, these are still rates that justify a Fed rate step in July, but anything after that is uncertain. Even though the FOMC signalled two further 25 bp rate hikes at the June meeting. As a result, the market is likely to increasingly price out this additional step, which it sees sceptically anyway, with any indication that inflation is falling even more quickly; that is likely to put pressure on the Dollar. 

If additionally, the economic data over the coming weeks suggest that the past rate steps are increasingly having an effect on the economy, not only is the last step going to be priced out but existing rate cut expectations are likely to increase further.