Theorem max1d

Description: A number is less than or equal to the maximum of it and another. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypotheses	max1d.1	|- ( ph -> A e. RR )
	max1d.2	|- ( ph -> B e. RR )
Assertion	max1d	|- ( ph -> A <_ if ( A <_ B , B , A ) )

Proof

Step	Hyp	Ref	Expression
1		max1d.1	|- ( ph -> A e. RR )
2		max1d.2	|- ( ph -> B e. RR )
3		max1	|- ( ( A e. RR /\ B e. RR ) -> A <_ if ( A <_ B , B , A ) )
4	1 2 3	syl2anc	|- ( ph -> A <_ if ( A <_ B , B , A ) )