Does the heap property in the definition of binary heaps apply recursively?

The definition of binary heaps says that it should be a complete binary tree and it should follow the heap property where according to the heap property, the key stored in each node is either greater than or equal to or less than or equal to the keys in the node’s children.

Binary tree

In the above tree, the node with value 70 is greater than its parent 10 breaking the heap property. However, 70 is also greater than 40 and lies in the subtree of 40. Will we say that the heap property is also breaking at 40, even though 40 is greater than its two children 10 and 2?