Theorem min2d

Description: The minimum of two numbers is less than or equal to the second. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Hypotheses	min2d.1	|- ( ph -> A e. RR )
	min2d.2	|- ( ph -> B e. RR )
Assertion	min2d	|- ( ph -> if ( A <_ B , A , B ) <_ B )

Proof

Step	Hyp	Ref	Expression
1		min2d.1	|- ( ph -> A e. RR )
2		min2d.2	|- ( ph -> B e. RR )
3		min2	|- ( ( A e. RR /\ B e. RR ) -> if ( A <_ B , A , B ) <_ B )
4	1 2 3	syl2anc	|- ( ph -> if ( A <_ B , A , B ) <_ B )