Let $A$ be a finite transition matrix, let $\Sigma_A$ be the associated one-sided topologically mixing subshift of finite type, and let $\sigma:\Sigma_A\to\Sigma_A$ be the left shift. Let $I\subset\mathbb{R}$ be an open interval, let $\alpha\in(0,1]$, and let $t\mapsto \beta_t$ be a real-analytic map from $I$ into $C^\alpha(\Sigma_A;\mathbb{R})$. If each $\beta_t$ has a unique equilibrium state and the Ruelle transfer operator associated to $\beta_t$ has a spectral gap on $C^\alpha(\Sigma_A;\mathbb{R})$ for every $t\in I$, then $t\mapsto P(\sigma,\beta_t)$ is real analytic on $I$. In particular, the family has no first-order pressure transition on $I$.