What's the correct implication between $\forall x(\,P(x) \vee Q(x)\,)$ and $\forall xP(x) \vee ∀xQ(x)$?
88281
Mixing and Distributing Qualifiers ($\forall x$, $\exists x$)
103112
Does the existential quantifier distribute over an implication?
109159
What's the intuition behind $(\exists y)(\mathscr{C}(y)\supset\mathscr{D})\supset((\forall x)\mathscr{C}(x)\supset\mathscr{D})$
49453
Why do I have to solve for $x$ in this proof, if I choose not to find a counterexample?
82739
Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?
35236
Proof $p \vdash q \Rightarrow p$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
31299
Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$?
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x
87955
How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $?
79407
How to solve ~(P → Q) : P & ~Q by natural deduction?
132423
Non trivial valuation over a finite extension $F/\mathbb{Q}_p$ is equivalent to the one induced by $v_p$
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
142762
how to prove that (P⊃Q)≡(¬Q⊃¬P) ( P ⊃ Q ) ≡ ( ¬ Q ⊃ ¬ P ) is disallowed in intuitionistic logic?
106799
Proof Verification: Converse of Intermediate Value Theorem
41044
Equivalence of $a \rightarrow b$ and $\lnot a \vee b$
148790
Basic question about proofs with the goal $\exists x P(x)$