Natural Deduction $(∀x∃y (P(x) → Q(y))) → (∃y∀x(P(x) → Q(y)))$
45481
Prove or disprove validity: $(\forall x \exists y (P(x) \supset Q(y))) \supset(\exists y \forall x (P (x) \supset Q(y)))$
139064
Show by using logical connectives laws that $(P\to Q) \land (Q \to R) $ is equivalent to $(P \to R) \land [(P \iff Q) \lor (R \iff Q)]$
106799
Proof Verification: Converse of Intermediate Value Theorem
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
5293
Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
142762
how to prove that (P⊃Q)≡(¬Q⊃¬P) ( P ⊃ Q ) ≡ ( ¬ Q ⊃ ¬ P ) is disallowed in intuitionistic logic?
31846
Does $\neg(x > y)$ imply that $y \geq x$?
6113
Proof of Strong principle of Induction (T. Tao Analysis I)
99911
How to show that if $x=(p,q)$ and $y=(p',q')$ then $x \sim y $ if $pq'=p'q$ is an equivalence relation?
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
15865
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
91861
Propositional Logic: p → q, ¬p → r, ¬q → ¬r ⊢ q
79024
the derivation of E(X|X)
15354
Formal proof of $\exists x \forall y P(x,y) \implies \forall y \exists x P(x,y)$
76635
Proof through combinatorial argument
134319
When induction proofs need a choice function
93410
How to prove ~ (~P & ~Q) : P ∨ Q by natural deduction