Your new example now contains a main verb (=, that is, equals), so what you have is correct.
But you can use either a semicolon or commas.
To use a "simpler" sentence:
1 We need to show that 2 plus 2 equals 4; that is, that 4 is the sum of
2 and 2.
2 We need to show that 2 plus 2, that is, the sum of 2 and 2, is [equals] 4.
Note the placement of the punctuation and of "that is".
In 1, we have two separate clauses, which we can join with a semicolon; the latter clause is clarifying, and can be removed without making the sentence ungrammatical.
In 2, we have a parenthetical statement. This is also clarifying and can also be removed without affecting the grammaticality or meaning.
A parenthetical statement can also use dashes or parentheses:
2a We need to show that 2 plus 2 – that is, the sum of 2 and 2 – is 4.
2b We need to show that 2 plus 2 (that is, the sum of 2 and 2) is 4.
Note that I have used en dashes in 2a; unspaced em dashes are generally preferred in American English.