Theorem 3brtr4g

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 16-Jan-1997)

	Ref	Expression
Hypotheses	3brtr4g.1	$$⊢\phi \to ARB$$
	3brtr4g.2	$$⊢C=A$$
	3brtr4g.3	$$⊢D=B$$
Assertion	3brtr4g	$$⊢\phi \to CRD$$

Proof

Step	Hyp	Ref	Expression
1		3brtr4g.1	$$⊢\phi \to ARB$$
2		3brtr4g.2	$$⊢C=A$$
3		3brtr4g.3	$$⊢D=B$$
4	2 3	breq12i	$$⊢CRD\leftrightarrow ARB$$
5	1 4	sylibr	$$⊢\phi \to CRD$$