Theorem tpr2uni

Description: The usual topology on ( RR X. RR ) is the product topology of the usual topology on RR . (Contributed by Thierry Arnoux, 21-Sep-2017)

	Ref	Expression
Hypothesis	tpr2tp.0	|- J = ( topGen ` ran (,) )
Assertion	tpr2uni	|- U. ( J tX J ) = ( RR X. RR )

Proof

Step	Hyp	Ref	Expression
1		tpr2tp.0	|- J = ( topGen ` ran (,) )
2	1	tpr2tp	|- ( J tX J ) e. ( TopOn ` ( RR X. RR ) )
3	2	toponunii	|- ( RR X. RR ) = U. ( J tX J )
4	3	eqcomi	|- U. ( J tX J ) = ( RR X. RR )