Theorem xnegred

Description: An extended real is real if and only if its extended negative is real. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	xnegred.1	|- ( ph -> A e. RR* )
Assertion	xnegred	|- ( ph -> ( A e. RR <-> -e A e. RR ) )

Proof

Step	Hyp	Ref	Expression
1		xnegred.1	|- ( ph -> A e. RR* )
2		xnegre	|- ( A e. RR* -> ( A e. RR <-> -e A e. RR ) )
3	1 2	syl	|- ( ph -> ( A e. RR <-> -e A e. RR ) )