There are signs in mathematics for "therefore" and "because," which are $\therefore$ and $\because$ respectively.
However, another frequently-used expression is "according to." Is there any symbol for that?
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No, there isn't, and it isn't good practice to use mathematical/formalistic symbols in the middle of a sentence.
"Now, Eq. (1) $\rightarrow$ that Eq. (2) is $\sim$ true,"
"Now, Eq. (1) implies that Eq. (2) is false,"
only makes the sentence more obscure. You could write out every sentence as a logical statement, but ask yourself, "what text would I rather read?" Your audience probably would choose the same.