B What Does the Notation = in Equivalence Classes Conclude to?

kidsasd987
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Please refer to the video at 37:02 from the link above.

I am struggling with the notation "=" of the property (a) which concludes to [a]=[m].
shouldn't it be [a]⊆[m], just like [m]⊆M.
 
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What does ##a \in [m]## mean? And what can be said about all elements ##b \sim a## if we use transitivity of ##\sim##?
In retrun, what does it mean for all elements ##c \sim m##?
 

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