How can I remove an all-zero column from a 3D array without reducing the dimensions

I'm trying to remove an all-zero column from a 3D array using numpy while maintaining the number of dimensions. I don't want to use trim either as the columns might not be at the edges of the array.

Intended functionality

I tried using ~np.all but that seems to strip away one of the dimensions:

import numpy as np

vals = [1,0,3,4,0,6,7,8,9,10,11,12]
array = np.reshape(vals, (2,2,3))

array:

[[[ 1  0  3]
  [ 4  0  6]]

 [[ 7  8  9]
  [10 11 12]]]

This is what I want to see:

[[[ 1  3]
  [ 4  6]]

 [[ 7  9]
  [10 12]]]

Let's break this up into multiple steps.

1. Use the astype method to convert the array to booleans. Columns of all False are 0s.
2. Use NOT on the array to convert columns of 0s from False to True.
3. Use all on axis 1 to perform a logical AND, which checks if a column is all 0s.
4. Use any on axis 0 to perform a logical OR, which collapses the result to get True or False values for each column in the array.
5. Use the NOT version of the result to index the last axis of the array to only get the columns that don't have the 0.

With labeled steps:

import numpy as np

vals = [1, 0, 3, 4, 0, 6, 7, 8, 9, 10, 11, 12]
array = np.reshape(vals, (2, 2, 3))
step1 = array.astype(bool)
step2 = ~step1
step3 = step2.all(1)
step4 = step3.any(0)
step5 = array[..., ~step4]

All together:

vals = [1, 0, 3, 4, 0, 6, 7, 8, 9, 10, 11, 12]
array = np.reshape(vals, (2, 2, 3))
res = array[..., ~(~array.astype(bool)).all(1).any(0)]
print(res)

Output:

[[[ 1  3]
  [ 4  6]]

 [[ 7  9]
  [10 12]]]