Remove all of one field from an array of fields in an entire collection

problem.js

/*
  I want to remove all the bool fields(inside the props array) from the following collection.
*/
//Initial state of collection
db.foos.find();
//#=>
{ "_id" : ObjectId("4d60699c768262073556634f"), "props" : [
	{
		"bool" : true,
		"name" : "bob"
	},
	{
		"bool" : false,
		"name" : "noah"
	}
] }
{ "_id" : ObjectId("4d6069a07682620735566350"), "props" : [
	{
		"bool" : true,
		"name" : "amos"
	},
	{
		"bool" : false,
		"name" : "miriam"
	}
] }



//Wanted state of collection
db.foos.find();
//#=>
{ "_id" : ObjectId("4d60699c768262073556634f"), "props" : [
	{
		"name" : "bob"
	},
	{
		"name" : "noah"
	}
] }
{ "_id" : ObjectId("4d6069a07682620735566350"), "props" : [
	{
		"name" : "amos"
	},
	{
		"name" : "miriam"
	}
] }