Metamath Proof Explorer
Description: Any element of a set is also an element of the sigmaalgebra that set
generates. (Contributed by Thierry Arnoux, 27Mar2017)


Ref 
Expression 

Assertion 
elsigagen 
$${\u22a2}\left({A}\in {V}\wedge {B}\in {A}\right)\to {B}\in \mathbf{\tau}\left({A}\right)$$ 
Proof
Step 
Hyp 
Ref 
Expression 
1 

sssigagen 
$${\u22a2}{A}\in {V}\to {A}\subseteq \mathbf{\tau}\left({A}\right)$$ 
2 
1

sselda 
$${\u22a2}\left({A}\in {V}\wedge {B}\in {A}\right)\to {B}\in \mathbf{\tau}\left({A}\right)$$ 