query: Problems understanding: $\Sigma \vdash \theta \text{ iff }\Sigma \vdash \forall x \theta$
positive_passages.docid: 20789
positive_passages.text: If $\Sigma \vdash \varphi$ then $\Sigma \vdash \forall x \varphi$. Why when $(\varphi \implies \forall x \varphi)$ is not true?
negative_passages.docid: 126862
negative_passages.text: Confused about $x \notin x$ example in Axiom of Specification
negative_passages.docid: 43551
negative_passages.text: Difficulty in understanding a part in a proof from Stein and Shakarchi Fourier Analysis book.
negative_passages.docid: 142594
negative_passages.text: Verifying the interpretation of stopping times and stopping time $\sigma$-algebras
negative_passages.docid: 42733
negative_passages.text: What's the difference between $\vdash$ and $\vDash$?
negative_passages.docid: 42355
negative_passages.text: Double check $G\sim H$ iff $G≈H$
negative_passages.docid: 20581
negative_passages.text: How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
negative_passages.docid: 135238
negative_passages.text: Time complexity function in terms of theta notation
negative_passages.docid: 132532
negative_passages.text: Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
negative_passages.docid: 152932
negative_passages.text: Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
negative_passages.docid: 129319
negative_passages.text: Weird "hidden answer" in $2\tan(2x)=3\text{cot}(x)$
negative_passages.docid: 62172
negative_passages.text: Why does $-b < a < b \iff |a| < b$?
negative_passages.docid: 129443
negative_passages.text: $f(\theta) = \cos \theta - \sqrt{3}\sin \theta$ in the form $r\sin(\theta-\alpha)$
negative_passages.docid: 31102
negative_passages.text: Why does $\frac{1}{r}\frac{dr}{d\theta} = \cot \psi$?
negative_passages.docid: 44285
negative_passages.text: What does this notation mean? F|U
negative_passages.docid: 52973
negative_passages.text: The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$
negative_passages.docid: 100335
negative_passages.text: Moving average process notation: negative or positive $\theta$s?