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No, pi bonds are formed when there's a double or triple bond. So in a double bond, one bond will be a sigma bond and the other will be a pi bond. In a triple bond, one bond will be a sigma bond and 2 would be pi bonds.
With that, any bond formed between two atoms, the sigma bond is formed first and there can only be one, with the double and triple bonds being composed of one sigma bond and one and two pi bonds.
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