grammar - Grammatical justification for でしかない

The song eX Dream by Myuji (which appears in an anime OP) contains the sentence:

[夢]{ゆめ}は夢でしかない

The general point of the sentence is fairly clear, meaning "a dream is just a dream". But what is the best way to think of the でしかない construction?

At first I saw it as 夢は夢で, as in, "a dream is a dream and...", but now I'm wondering how correct this is or if it's correct at all.

Is it better to look at it as a separation of the parts of である? Does this happen in many other cases, where you use a qualified で followed by ある?

Answer

Let's start with something common:

夢は夢だ。 'Dreams are dreams.'

Let's negate it (using ではない instead of its contracted form じゃない):

夢は夢ではない。 'Dreams are not dreams.'

は is a 係助詞{かかりじょし} ("binding particle"). Any 係助詞 fits in this spot. しか is also a 係助詞:

夢は夢でしかない。'Dreams are nothing but dreams.'

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The "modern" grammatical analysis of this stuff is that で is the 連用形{れんようけい} ("continuative form") of the copula だ which results in ではない and でしかない falling nicely into this general rule:

(連用形 of something) + (optional 係助詞) + (ない or ある)

Some other instances of this rule are すごく（は）ない、あつく（も）ない、バカで（も）ある。