Theorem eqled

Description: Equality implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	eqled.1	|- ( ph -> A e. RR )
	eqled.2	|- ( ph -> A = B )
Assertion	eqled	|- ( ph -> A <_ B )

Proof

Step	Hyp	Ref	Expression
1		eqled.1	|- ( ph -> A e. RR )
2		eqled.2	|- ( ph -> A = B )
3		eqle	|- ( ( A e. RR /\ A = B ) -> A <_ B )
4	1 2 3	syl2anc	|- ( ph -> A <_ B )