Role of Dominant 7th chord in particular progressions

Question

Examining this progression in F:

 | F | A7 | Dm7 | Bb, Bbm |

 | F, E7 | Gm7, C7 | F, D7 | Gm7, C7 |

In the fifth measure I really don't understand what role has the E7 chord because I can't identify as:

• primary dominant - it isn't on the fifth degree of the scale
• secondary dominant - it doesn't resolve to his relative first degree (Am7)
• tritone substitution - it does not resolve to Eb his relative IIb

So what is the role of the chord?

Answer 1

It's just a passing chord on the way to Gm7 from F.

From Gm7 to E7 the D is common and the other notes are moving chromatically to get to Gm7. If you look at the notes each contain you'll see:

F -> E  -> F
A -> G# -> G
C -> B  -> Bb
C -> D  -> D

You'll notice the chromatic descending line in A to G and C to Bb and The F - E - F can be looked at as a neighboring tone.

Answer 2

In F major the subdominant chord is Bb7, and E7 is the tritone substitution of that chord.

The tritone interval G#-D appears in both chords.

In the E7 chord the G# functions as the 3rd and the D functions as the 7th.

And if you respell G# as Ab then the same interval Ab-D appears in the Bb7 chord, the Ab functions as the 7th and the D functions as the 3rd.