The bridge theme is extended with modulatory changes.
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Now it is the violins' turn to take the lead. In fact, they elaborate the horn's melody through an ascending sequence, which produces great tension and expectation.
By changing the F note to a F-sharp note, we can clearly feel that Beethoven is preparing to lead us to a new key, the key of G major (which is the dominant of C major). This should not come as a surprise to us, since in the traditional sonata form this must happen. When the first theme is in a minor key (as in the first movement), the second theme is usually introduced in the relative major. However, when the first theme is in a major key (as in this movement), then the second theme is usually written in its major dominant, which is, in this case, G major.
If, in fact, this is what is about to happen, then we can try to answer the question about the passage. Is it a second theme or a bridge leading to the second theme? It seems that it is more a bridge than a theme. But, as it has a clear melodic strain, which is easy to sing and remember, we can agree upon a "bridge theme".
