Is $\exists x(P(x)\rightarrow\forall y P(y))$ a tautology?
1027
Why is this true? $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$
87955
How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $?
47161
Quick logic question about $P\leftrightarrow Q$, terminology
5313
Existence of how many sets is asserted by the axiom of choice in this case?
42150
Prove that $\forall x \neg P(x) \iff \neg \exists x P(x)$
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
51369
Natural deduction proof of $p \lor (p\implies q)$ with propositional calculus
32325
Can there be a valid argument which has a tautology as a conclusion?
124424
How to show that there is a deduction of $\varphi\leftrightarrow\psi$
119888
Is it possible to convert $\forall$ quantifiers to $\exists$ quantifiers without negation?
43655
Verify is tautology by using logical equivalence
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
5639
No \xrightrightarrow[a]{b}?
84251
Show that $\Gamma \cup \{\neg \phi\}$ is satisfiable if and only if $\Gamma\not \models \phi$
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?