MHB What Does the Inequality x >= y Mean?

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∀x∀y (x >= y)
 
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WannaBe said:
∀x∀y (x >= y)

For all $x$ and for all $y,$ $x$ is greater or equal than $y.$
 
For any pair $$(x,y)$$ the inequality $$x\geq y$$ holds.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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