Final Answer:
No, the act of breathing is a posteriori knowledge, not a priori.
Explanation:
While the premise "I exist" (P1) might be seen as a priori based on self-awareness or intuition, the deduction that "I am respirating" (C1) relies on empirical observation or sensory experience, making it a posteriori knowledge. The link between existence and respiration (P2) is based on empirical evidence and observation of biological functions rather than being self-evident through pure reasoning.