--snip--
In Bitcoin Core, this was done simply-I delete the transaction from the mempool, and then conduct a new one with a higher Commission, as soon as it passed - the old one will not be held and will be discarded in any case by all nodes
Either the transaction had a rbf flag, it wasn't broadcasted, you waited untill the original transaction was dropped from the mempool of most of the other nodes, the first transaction was invalid or you got extremely lucky.
Anyways, removing a broadcasted, valid, transaction from your own mempool does not remove it from the mempool of any other node.