Metamath Proof Explorer

Theorem eqtr

Description: Transitive law for class equality. Proposition 4.7(3) of TakeutiZaring p. 13. (Contributed by NM, 25-Jan-2004)

Ref Expression
Assertion eqtr 
|- ( ( A = B /\ B = C ) -> A = C )

Proof

Step Hyp Ref Expression
1 eqeq1 
 |-  ( A = B -> ( A = C <-> B = C ) )
2 1 biimpar 
 |-  ( ( A = B /\ B = C ) -> A = C )