Um, no, it's not. If the amount of calories you burn decreases more than the calories they intake, for example, you might not lose weight. You might even gain weight.
And that's the point -- calories burned is not a constant. It changes a great deal, and it's very common for the body to respond to less calories in, by burning less calories.
To test the truth, try the converse. If you eat more, will you gain weight? Most of us would agree this is an obvious truism.
Or take the limit. If you eat nothing, will you lose weight? Obviously you will.
The question exists because folks want to eat as much as they can, and also lose weight. Give in to thermodynamics, eat very little, and lose weight as quickly as you like. That's chemistry and physics right there.
Again, nope. If you're ~50 lbs overweight, and then cut out starches and sugars, replacing them with protein and fat, but increase your overall calorie intake slightly, there's still a good chance you will lose weight.
So, not an obvious truism, but actually incorrect.
And that's the point -- calories burned is not a constant. It changes a great deal, and it's very common for the body to respond to less calories in, by burning less calories.