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To answer you very precisely, start thinking Yoga as the Art of Living.
I never tried to connect with the explicit spiritual side of yoga.
Because you never tried, doesn't mean you won't connect or won't find 'the Yuj', which is simply a harmonious connection of your body with the mind. I'm sure you must've felt it by practicing yoga.
For what you're referring by spirituality may be something like the summit of it. I may better answer you if I can understand your view of spirituality.