I have a linear regression model for a dependent variable $Y$ based on two independent variables, $X1$ and $X2$, so I have a general form of a regression equation
$Y = A + B_1 \cdot X_1 + B_2 \cdot X_2 + \epsilon$,
where $A$ is the intercept, $\epsilon$ is the error term, and $B_1$ and $B_2$ are the respective coefficients of $X_1$ and $X_2$. I perform a multiple regression with software (statsmodel in Python) and I get coefficients for the model: $A = a, B_1 = b_1, B_2 = b_2$. The model also gives me $p$ values for each coefficient: $p_a$, $p_1$, and $p_2$. My question is: What is the null hypothesis for those individual $p$ values? For example, to obtain $p_1$ I know that the null hypothesis entails a 0 coefficient for $B_1$, but what about the other variables? In other words, If the null hypothesis is $Y = A + 0 \cdot X_1 + B_2 \cdot X_2$, what are the values of $A$ and $B_2$ for the null hypothesis from which the $p$-value for $B_1$ is derived?