Metamath Proof Explorer


Theorem opnssborel

Description: Open sets of a generalized real Euclidean space are Borel sets (notice that this theorem is even more general, because X is not required to be a set). (Contributed by Glauco Siliprandi, 3-Jan-2021)

Ref Expression
Hypotheses opnssborel.a
|- A = ( TopOpen ` ( RR^ ` X ) )
opnssborel.b
|- B = ( SalGen ` A )
Assertion opnssborel
|- A C_ B

Proof

Step Hyp Ref Expression
1 opnssborel.a
 |-  A = ( TopOpen ` ( RR^ ` X ) )
2 opnssborel.b
 |-  B = ( SalGen ` A )
3 1 fvexi
 |-  A e. _V
4 2 sssalgen
 |-  ( A e. _V -> A C_ B )
5 3 4 ax-mp
 |-  A C_ B