Theorem eqnbrtrd

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

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

Proof

Step	Hyp	Ref	Expression
1		eqnbrtrd.1	|- ( ph -> A = B )
2		eqnbrtrd.2	|- ( ph -> -. B R C )
3	1	breq1d	|- ( ph -> ( A R C <-> B R C ) )
4	2 3	mtbird	|- ( ph -> -. A R C )