No deity but Him: three pieces, one mechanism
The formula لَآ إِلَٰهَ إِلَّا هُوَ works in three steps: لا negates every deity, إلا withdraws a single exception from that negation, and هو designates what remains. It is proof by subtraction applied to oneness.
First step, the particle لا: a total negation, emptying the category "deity" of all it could contain.
Second step, the particle إلا: an exception, subtracting a single element from that negation.
Third step, the pronoun هو: it receives what remains, and refers back to God named just before. "God, there is no deity but Him, the Living, the Self-Subsisting" (2:255).
The formula does not affirm first; it denies everything, then lets only one remain. This is exactly the mechanism described in “Proof by subtraction”. The corpus uses the construction لا إله إلا in 37 phrases.
In the text
ٱللَّهُ لَآ إِلَٰهَ إِلَّا هُوَ ٱلْحَىُّ ٱلْقَيُّومُ