Theorem 3brtr3g

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

	Ref	Expression
Hypotheses	3brtr3g.1	$$⊢\phi \to ARB$$
	3brtr3g.2	$$⊢A=C$$
	3brtr3g.3	$$⊢B=D$$
Assertion	3brtr3g	$$⊢\phi \to CRD$$

Proof

Step	Hyp	Ref	Expression
1		3brtr3g.1	$$⊢\phi \to ARB$$
2		3brtr3g.2	$$⊢A=C$$
3		3brtr3g.3	$$⊢B=D$$
4	2 3	breq12i	$$⊢ARB\leftrightarrow CRD$$
5	1 4	sylib	$$⊢\phi \to CRD$$