Showing Equivalence between a Proposition and the Axiom of Choice
21202
Axiom of choice is equivalent to every relation includes a function with the same domain
94295
Pigeonhole-principle with two choices
43655
Verify is tautology by using logical equivalence
115675
Strange consequences of Axiom of Choice in Zermelo set theory
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
91861
Propositional Logic: p → q, ¬p → r, ¬q → ¬r ⊢ q
134319
When induction proofs need a choice function
83757
Is the following equivalent to the axiom of choice?
48213
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
154832
Show that there is always a proposition between two propositions logic
144899
Do We Need the Axiom of Choice for Finite Sets?
56191
How to demystify the axioms of propositional logic?
142840
Open axioms of equality
108367
proving tautologically equivalent
136883
The class of equivalence.
48615
Does the assertion that every two cardinalities are comparable imply the axiom of choice?
118189
Proving the pairing axiom from the rest of ZF