query: Definition of 'term t is free for v in $\phi$' in predicate logic
positive_passages.docid: 27506
positive_passages.text: What does it mean for a variable to be free for something?
negative_passages.docid: 99480
negative_passages.text: Why is predicate "all" as in all(SET) true if the SET is empty?
negative_passages.docid: 48368
negative_passages.text: Prove using Natural Deduction in predicate logic $(\forall x\ P(x))\to Q ⊢ \exists x (P(x)\to Q)$
negative_passages.docid: 32244
negative_passages.text: Propositional Logic - Deduction
negative_passages.docid: 46423
negative_passages.text: Distributivity of quantifiers over logical connectives
negative_passages.docid: 126870
negative_passages.text: Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]
negative_passages.docid: 149907
negative_passages.text: $T\circ T=0:V\rightarrow V \implies R(T) \subset N(T)$
negative_passages.docid: 116978
negative_passages.text: Trying to prove $p,p \to (r \to q) \vdash (\neg q \to \neg r)$ by using natural deduction.
negative_passages.docid: 148239
negative_passages.text: natural deduction proof with De Morgan's laws
negative_passages.docid: 132532
negative_passages.text: Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
negative_passages.docid: 100844
negative_passages.text: How should I understand "$A$ unless $B$"?
negative_passages.docid: 49385
negative_passages.text: 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
negative_passages.docid: 151038
negative_passages.text: How to prove (A v B), (A → C), (B → D) therefore (C v D)
negative_passages.docid: 113605
negative_passages.text: In Fitch, how does one prove "(P → Q)" from the premise "(¬P ∨ Q)"?
negative_passages.docid: 111862
negative_passages.text: Proof for sequent (Logic)
negative_passages.docid: 131132
negative_passages.text: Proofs using vector properties
negative_passages.docid: 150041
negative_passages.text: T must be contravariantly valid