Metamath Proof Explorer


Theorem eqbrtrrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 17-Sep-2004)

Ref Expression
Hypotheses eqbrtrrid.1 𝐵 = 𝐴
eqbrtrrid.2 ( 𝜑𝐵 𝑅 𝐶 )
Assertion eqbrtrrid ( 𝜑𝐴 𝑅 𝐶 )

Proof

Step Hyp Ref Expression
1 eqbrtrrid.1 𝐵 = 𝐴
2 eqbrtrrid.2 ( 𝜑𝐵 𝑅 𝐶 )
3 eqid 𝐶 = 𝐶
4 2 1 3 3brtr3g ( 𝜑𝐴 𝑅 𝐶 )