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Next up add the taps, unlink the old PHP and add the new!

brew tap homebrew/dupes
brew tap homebrew/versions
brew tap homebrew/homebrew-php
brew unlink php56
brew install php70

And the result?

php -v

PHP 7.0.27 (cli) (built: Jan  5 2018 12:26:39) ( NTS )
Copyright (c) 1997-2017 The PHP Group
Zend Engine v3.0.0, Copyright (c) 1998-2017 Zend Technologies

Voilà!