Network Disruption: A nuclear holocaust could disrupt the global telecommunications and internet infrastructure, making it challenging for Bitcoin users to access the network. Miners, who maintain the network, may struggle to operate without a stable power supply and internet access.

Blockchain Integrity: The Bitcoin blockchain itself is decentralized and distributed across many nodes worldwide. If some nodes survive and maintain copies of the blockchain, it might be possible to rebuild the network when communication infrastructure is restored. The integrity of the blockchain would depend on the survivability of these nodes.

Localized Use: In isolated pockets where infrastructure remains intact, individuals with the necessary hardware and connectivity might continue to use and trade Bitcoin in a limited, peer-to-peer fashion.

Long-Term Viability: In the long term, the viability of Bitcoin and other cryptocurrencies in a post-apocalyptic world is uncertain. Survivors would likely prioritize more immediate concerns such as food, water, and shelter, rather than digital currencies.

Alternative Systems: In extreme scenarios, communities might develop alternative systems of trade and barter, as physical goods and resources become more important than digital assets.