Metamath Proof Explorer

Theorem eqtr2id

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

Ref Expression
Hypotheses eqtr2id.1 
|- A = B
eqtr2id.2 
|- ( ph -> B = C )
Assertion eqtr2id 
|- ( ph -> C = A )

Proof

Step Hyp Ref Expression
1 eqtr2id.1 
 |-  A = B
2 eqtr2id.2 
 |-  ( ph -> B = C )
3 1 2 eqtrid 
 |-  ( ph -> A = C )
4 3 eqcomd 
 |-  ( ph -> C = A )