Proof of $\Box (A\land B) \leftrightarrow \Box A \land \Box B$ in propositional modal logics
117661
Distribution Axiom of Modal Logic
32009
Prove $\;\big((p\rightarrow q) \lor (p \rightarrow r)\big) \rightarrow (q\lor r)\equiv p \lor q \lor r$ without use of a truth table.
77759
How do i prove that $(p \vee q) \wedge (\neg p \vee r) \rightarrow (q \vee r)$ is a tautology without using the truth table?
47161
Quick logic question about $P\leftrightarrow Q$, terminology
15504
In classical logic, why is $(p\Rightarrow q)$ True if $p$ is False and $q$ is True?
140194
Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$
82739
Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?
49385
Proving $\forall x (A\to B) \to(A \to \forall x B):x\notin \mbox{free}(A)$ in a Hilbert system where it is not an axiom
46613
What's the difference between $\equiv$ and $\leftrightarrow$ in a formal proof?
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
35236
Proof $p \vdash q \Rightarrow p$
59644
Proof of Cartesian product intersection
87928
Proof of logical equivalence of biconditional and other proposition
72034
Truth table and the meaning of $\oplus$ in propositional logic
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
150738
Proof of $(A - B) - C = A - (B \cup C)$