Theorem eqbrtr

Description: Substitution of equal classes in binary relation. (Contributed by Peter Mazsa, 14-Jun-2024)

	Ref	Expression
Assertion	eqbrtr	⊢ ( ( 𝐴 = 𝐵 ∧ 𝐵 𝑅 𝐶 ) → 𝐴 𝑅 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		breq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 𝑅 𝐶 ↔ 𝐵 𝑅 𝐶 ) )
2	1	biimpar	⊢ ( ( 𝐴 = 𝐵 ∧ 𝐵 𝑅 𝐶 ) → 𝐴 𝑅 𝐶 )