Theorem brneqtrd

Description: Substitution of equal classes into the negation of a binary relation. (Contributed by Glauco Siliprandi, 3-Jan-2021)

	Ref	Expression
Hypotheses	brneqtrd.1	|- ( ph -> -. A R B )
	brneqtrd.2	|- ( ph -> B = C )
Assertion	brneqtrd	|- ( ph -> -. A R C )

Proof

Step	Hyp	Ref	Expression
1		brneqtrd.1	|- ( ph -> -. A R B )
2		brneqtrd.2	|- ( ph -> B = C )
3	2	breq2d	|- ( ph -> ( A R B <-> A R C ) )
4	1 3	mtbid	|- ( ph -> -. A R C )