Metamath Proof Explorer

Theorem eqtr4id

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998)

Ref Expression
Hypotheses eqtr4id.2 
|- A = B
eqtr4id.1 
|- ( ph -> C = B )
Assertion eqtr4id 
|- ( ph -> A = C )

Proof

Step Hyp Ref Expression
1 eqtr4id.2 
 |-  A = B
2 eqtr4id.1 
 |-  ( ph -> C = B )
3 1 eqcomi 
 |-  B = A
4 2 3 eqtr2di 
 |-  ( ph -> A = C )