How can I deduce the existence of $2^X$ from the powerset axiom
52614
(exercise from Tao's analysis book) Proof of a lemma relating to power set of X
22687
Proof of the power rule for logarithms
43048
When is $2^n \pm 1$ a perfect power
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
63313
Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$
148790
Basic question about proofs with the goal $\exists x P(x)$
3465
Equivalence relations and power sets.
130093
Prove by Induction : $n < 2^n$
60216
Power Set Explanation
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
47697
Russell's paradox: a set cannot contain its own powerset
42314
Without appealing to choice, can we prove that if $X$ is well-orderable, then so too is $2^X$?
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
36612
Strange set notation (a set as a power of 2)?
14161
Proof of when is $A=X^TX$ invertible?
116501
How to show equinumerosity of  the powerset of $A$ and the set of functions from $A$ to $\{0,1\}$ without cardinal arithmetic?
114185
Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$