When writing a proof, why do we want to assume a different but equivalent condition given in the proposition?
3285
In proof by induction, what does it mean when condition for inductive step is lesser than the propsition itself?
40655
Propositional Logic - Can you Derive $C \to A$ from $A$ alone, given the introduction rule?
61303
"Infer" vs. "imply" — can "infer" imply "imply"?
93557
Intuitively, why does (B → S) ≡ (¬B ∨ S)?
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
141814
Proofs using theorems instead of axioms
36726
How Implication or Material/Concrete Conditional works when the antecedent is false and the consequent is true
70166
Why is the universal quantifier $\forall x \in A : P(x)$ defined as $\forall x (x \in A \implies P(x))$ using an implication?
21035
Clarifying on how if p,q is logically equivalent to p only if q
13064
In what order are chained implications evaluated? (i.e. $a \implies b \implies c$)
98271
Why does $(x \to a) ≠ (x = a)$ , But $f(x \to a) = f(x = a)$
157490
Statements equivalent to the Axiom of Choice
109858
How could a statement be true without proof?
113065
Proving equivalences of statements equivalent to AC
73253
Question About equal signs in Theorems
56351
Prove that these statements $(A \lor \neg B)$ and $\neg A \to \neg B$ are logically equivalent
83714
$A \in B$ vs. $A \subset B$ for proofs