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With modifier: We were going on an air-to-air photo mission.

Without: We were going on our first air to air.

OR

We were going on our first air-to-air.

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It should stay hyphenated, I think. It's still a phrasal adjective, modifying a noun that is now implied; it just turns into a nominalized adjective when the noun is removed.

Note that it's the adjectives that modify the noun here, not vice versa. Unless I misunderstood what you mean by modifier.

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