Prove the Axiom of Replacement implies the Axiom of Specification.
35123
How do the separation axioms follow from the replacement axioms?
21202
Axiom of choice is equivalent to every relation includes a function with the same domain
51369
Natural deduction proof of $p \lor (p\implies q)$ with propositional calculus
10598
Contrapositive Fitch Proof
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
76635
Proof through combinatorial argument
120311
Equivalence of Axiom of Regularity
53025
Why the need of Axiom of Countable Choice?
17363
Prove that the intersection of two equivalence relations is an equivalence relation.
132287
Axiom of Choice and Right Inverse
131889
Axiom of choice and calculus
142219
Does the splitting lemma hold without the axiom of choice?
9158
Proving that a propositional theory of any cardinality has an independent set of axioms
49385
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
48030
Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?