Axiom of extensionality - why can't we replace $\Rightarrow$ with $\iff$?
59820
ZF Extensionality axiom
134384
What does $\rightarrow$ mean in $p \rightarrow q$
103112
Does the existential quantifier distribute over an implication?
42869
Is $\lor$ definable in intuitionistic logic?
93761
"if", and "elif" chain versus a plain "if" chain
157490
Statements equivalent to the Axiom of Choice
20252
The Axiom of Choice and the Cartesian Product.
153935
A weaker Axiom of Infinity?
46160
What is the difference between implication symbols: $\rightarrow$ and $\Rightarrow$?
100844
How should I understand "$A$ unless $B$"?
1027
Why is this true? $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$
84378
Does axiom of foundation/regularity protect against Russell-like paradoxes?
2342
How does equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ in $\sf{ZF}$ relate to the axiom of choice?
132287
Axiom of Choice and Right Inverse
121847
Don't we need the axiom of choice to choose from a non-empty set?
152272
Can you explain the "Axiom of choice" in simple terms?
88281
Mixing and Distributing Qualifiers ($\forall x$, $\exists x$)