A somewhat infamous law (to me at least), that states:

$$a.A_{eq}=b.B_{eq}=c.C_{eq}=d.D_{eq}$$

for any and every balanced chemical equation -

$$a.A+b.B = c.C+d.D$$

where $i$ denotes the stoichiometric coefficient(/no. of moles) of the chemical species $I$ and $I_{eq}$ denotes the number of equivalents in 1 mole(/formula mass...?) of the chemical species $I$.

Am I wrong about any of the facts I've presented above? Please mention any errors you spot.

Assuming that I did fine, my simple question is,

What's the mathematical proof for this law?

I tried surfing online, but all I came across (with my not-so-deep searches) were verbal explanations of the law.

Is there no mathematical proof to this law whatsoever? I'll be satisfied to just find a proof, even if I don't understand the complicated math going into it (for I'm an eleventh grader).