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 φ B R C
Assertion eqbrtrrid φ A R C

Proof

Step Hyp Ref Expression
1 eqbrtrrid.1 B = A
2 eqbrtrrid.2 φ B R C
3 eqid C = C
4 2 1 3 3brtr3g φ A R C