Metamath Proof Explorer

Theorem eqtr4di

Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses eqtr4di.1 
|- ( ph -> A = B )
eqtr4di.2 
|- C = B
Assertion eqtr4di 
|- ( ph -> A = C )

Proof

Step Hyp Ref Expression
1 eqtr4di.1 
 |-  ( ph -> A = B )
2 eqtr4di.2 
 |-  C = B
3 2 eqcomi 
 |-  B = C
4 1 3 syl6eq 
 |-  ( ph -> A = C )