Rule 708.4 · Face-Down Spells and Permanents

Objects that are cast face down are turned face down before they are put onto the stack, so effects that care about the characteristics of a spell will see only the face-down spell’s characteristics. Any effects or prohibitions that would apply to casting an object with these characteristics (and not the face-up object’s characteristics) are applied to casting this object. The permanent the spell becomes will be a face-down permanent.

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The life counter has an AI judge that answers your play citing the exact rules. It is part of Gatewatch Pro; the rules, Oracle text and rulings stay free.