Theorem xrgtned

Description: 'Greater than' implies not equal. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypotheses	xrgtned.1	|- ( ph -> A e. RR* )
	xrgtned.2	|- ( ph -> B e. RR* )
	xrgtned.3	|- ( ph -> A < B )
Assertion	xrgtned	|- ( ph -> B =/= A )

Proof

Step	Hyp	Ref	Expression
1		xrgtned.1	|- ( ph -> A e. RR* )
2		xrgtned.2	|- ( ph -> B e. RR* )
3		xrgtned.3	|- ( ph -> A < B )
4		xrltne	|- ( ( A e. RR* /\ B e. RR* /\ A < B ) -> B =/= A )
5	1 2 3 4	syl3anc	|- ( ph -> B =/= A )