query: How to prove that $(P \supset Q) \equiv (\neg Q \supset \neg P)$is disallowed in intuitionistic logic?
positive_passages.docid: 142762
positive_passages.text: how to prove that (P⊃Q)≡(¬Q⊃¬P) ( P ⊃ Q ) ≡ ( ¬ Q ⊃ ¬ P ) is disallowed in intuitionistic logic?
negative_passages.docid: 124424
negative_passages.text: How to show that there is a deduction of $\varphi\leftrightarrow\psi$
negative_passages.docid: 123458
negative_passages.text: Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
negative_passages.docid: 139064
negative_passages.text: Show by using logical connectives laws that $(P\to Q) \land (Q \to R) $ is equivalent to $(P \to R) \land [(P \iff Q) \lor (R \iff Q)]$
negative_passages.docid: 126633
negative_passages.text: Is a contradiction enough to prove a set equality to $\varnothing$?
negative_passages.docid: 150053
negative_passages.text: Is "$(P \land Q) \to P$" a tautology?
negative_passages.docid: 86154
negative_passages.text: Why is this true? A set is Dedekind infinite if and only if equipotent to the union with the set containing itself
negative_passages.docid: 19811
negative_passages.text: $(P(X), C_R)$ may be a choice structure even if $R$ is not a rational relation.
negative_passages.docid: 143627
negative_passages.text: Use the Fitch system to prove the tautology (p ∨ ¬p)
negative_passages.docid: 85770
negative_passages.text: What is the difference between ∀x(p(x) →q(x)) and ∀x(p(x) ∧q(x))?
negative_passages.docid: 70166
negative_passages.text: Why is the universal quantifier $\forall x \in A : P(x)$ defined as $\forall x (x \in A \implies P(x))$ using an implication?
negative_passages.docid: 65895
negative_passages.text: Irrationality proofs not by contradiction
negative_passages.docid: 70117
negative_passages.text: Show that $(p \to q) \lor (q \to p)$ is a tautology
negative_passages.docid: 10598
negative_passages.text: Contrapositive Fitch Proof
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 126713
negative_passages.text: Strong induction and vacuous truth
negative_passages.docid: 84251
negative_passages.text: Show that $\Gamma \cup \{\neg \phi\}$ is satisfiable if and only if $\Gamma\not \models \phi$