query: Proving two statements about the axiom of choice are equivalent
positive_passages.docid: 20252
positive_passages.text: The Axiom of Choice and the Cartesian Product.
negative_passages.docid: 131889
negative_passages.text: Axiom of choice and calculus
negative_passages.docid: 130998
negative_passages.text: Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
negative_passages.docid: 108045
negative_passages.text: Show that are logically equivalent
negative_passages.docid: 35123
negative_passages.text: How do the separation axioms follow from the replacement axioms?
negative_passages.docid: 78290
negative_passages.text: Countable axiom of choice: why you can't prove it from just ZF
negative_passages.docid: 53025
negative_passages.text: Why the need of Axiom of Countable Choice?
negative_passages.docid: 88736
negative_passages.text: How does the Axiom of Extensionality prove the uniqueness of Specified sets?
negative_passages.docid: 113065
negative_passages.text: Proving equivalences of statements equivalent to AC
negative_passages.docid: 83714
negative_passages.text: $A \in B$ vs. $A \subset B$ for proofs
negative_passages.docid: 17624
negative_passages.text: Axiom of Choice iff Every set has a choice function
negative_passages.docid: 66548
negative_passages.text: proving topological equivalence
negative_passages.docid: 142219
negative_passages.text: Does the splitting lemma hold without the axiom of choice?
negative_passages.docid: 84562
negative_passages.text: Proof using only field axioms
negative_passages.docid: 150790
negative_passages.text: Prove two sets have same Cardinality by writing down bijection
negative_passages.docid: 138897
negative_passages.text: help with some Hilbert style proofs in a propositional logic axiom system.
negative_passages.docid: 49220
negative_passages.text: Open Sets of $\mathbb{R}^1$ and axiom of choice