# Proving in first order logic for some arbitrary valuations of sigma in Machover's text

#### pooj4

##### New member
Trouble working through Set theory, Logic, and their Limitations by Maurice Machover. Particularly these

1. $\sigma \vDash \alpha \rightarrow \forall x\alpha$ where $x$ does not occur in a free $\alpha$

2. $\sigma \vDash s_1 = t_1 \rightarrow ... \rightarrow s_n = t_n \rightarrow fs_1...s_n=ft_1...t_n$

3. $\sigma \vDash \forall x \alpha \rightarrow \alpha(x/t)$ (appealing to the fact that generally $\alpha(x/t)^\sigma = {\alpha}^{\sigma(x/t^\sigma )})$

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
What exactly has to be done?