Not just all prophets, everyone is alive, just not alive on earth.
From Qur'an:
Ali 'Imran: 169:
وَلَا تَحْسَبَنَّ الَّذِينَ قُتِلُوا فِي سَبِيلِ اللَّهِ أَمْوَاتًا ۚ بَلْ أَحْيَاءٌ عِندَ رَبِّهِمْ يُرْزَقُونَ
And do not ever reckon the ones who have been killed in the way of Allah (as) dead; no indeed, they are alive in the Providence of their Lord, by Him provided.
Salaam at the end of Salat:
السلام علیک ایها النبی و رحمه الله و برکاته
Peace be unto you O prophet and the mercy and all blessings of God
The above shows that the prophet while not being a martyr is alive. If he was to be assumed dead then we should have said: السلام عليه و رحمت الله
Narrated from Imam Kazim:
«انه روی فی الکافی باسناده عن ابی الحسن الکاظم علیه السلام انه قال فی
قصة لمنکری المعاد من الامم الماضیة فاحدث الله فیهم الاحلام و لم یکن
قبل ذلک فاتوا نبیهم فاخبروه بما راو و ما انکروا من ذلک فقال: ان الله
تعالی اراد ان یحتج علیکم بهذا هکذا تکون ارواحهم اذا متم و ان بلیت
ابدانکم تصیر الارواح الی عقاب تبعث الابدان »
Al-Kafi Vol. 1 Pg. 110 [...Imam Kazim was talking about the previous
nations who were denying the judgement day: Allah had placed
'sleeping' among them while they were asking from their prophets to
show them examples of what will happen after death]
Allah has ordained to reason with you using 'sleep', as your souls
will depart your bodies just as they do when you go sleep and by the
will of Allah they will be joined with your body again to see the
divine retribution
Do we do die will we go to sleep? No. Do we die die (like we are non-existent like what the atheists say) when we are put into our graves? Again no, it's just beginning of our real life.
Narrated from Prophet Muhammad:
النَّاسِ نِیَامٌ فَإِذَا مَاتُوا انْتَبَهُوا
People are sleep, once they die they are awaken.
