As your variable names already suggested, you may use all(...)
:
numbers = [1, 25, 31, 42, 45, 52, 59, 63, 66, 70]
allnumbers = [1, 2, 9, 25, 26, 30, 31, 35, 42, 49, 45, 51, 52, 55, 59, 60, 63, 65, 66, 70]
if (all(number in allnumbers for number in numbers)):
print("Yes")
Another variant would include using sets:
smaller_list = set(numbers)
bigger_list = set(allnumbers)
if biggerlist.intersection(smaller_list) == smaller_list:
print("yes")
To see, how many numbers have matched, use:
numbers_matched = len(bigger_list.intersection(smaller_list))
See a demo on ideone.com.