This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem eqbrtrrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006)

Ref Expression
Hypotheses eqbrtrrdi.1 
|- ( ph -> B = A )
eqbrtrrdi.2 
|- B R C
Assertion eqbrtrrdi 
|- ( ph -> A R C )

Proof

Step Hyp Ref Expression
1 eqbrtrrdi.1 
 |-  ( ph -> B = A )
2 eqbrtrrdi.2 
 |-  B R C
3 1 eqcomd 
 |-  ( ph -> A = B )
4 3 2 eqbrtrdi 
 |-  ( ph -> A R C )