diff --git a/theorems/T000534.md b/theorems/T000534.md
index ceb657ef3..6d9b20a97 100644
--- a/theorems/T000534.md
+++ b/theorems/T000534.md
@@ -2,10 +2,16 @@
 uid: T000534
 if:
   and:
-  - P000016: true
+  - P000019: true
   - P000112: true
 then:
   P000053: true
 ---
 
-A compact space does not have a strictly coarser $T_2$ topology.
+Let $f \colon X \to Y$ be a continuous bijection from a {P19} space $X$ to a {P53} space $Y$.
+
+Let $A \subseteq X$ be closed.
+Since closed subspaces and continuous images of a {P19} space are {P19}, $f(A)$ is {P19}.
+Since $Y$ is {P53}, it is {P103} [(Explore)](https://topology.pi-base.org/spaces?q=Metrizable+%2B+%7EStrongly+KC), and hence $f(A)$ is closed in $Y$.
+
+Therefore, $f$ is a closed map and $f$ is a homeomorphism, which implies $X$ itself is {P53}.