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Metamath Proof Explorer

Theorem eqtr2d

Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999)

Ref Expression
Hypotheses eqtr2d.1 
|- ( ph -> A = B )
eqtr2d.2 
|- ( ph -> B = C )
Assertion eqtr2d 
|- ( ph -> C = A )

Proof

Step Hyp Ref Expression
1 eqtr2d.1 
 |-  ( ph -> A = B )
2 eqtr2d.2 
 |-  ( ph -> B = C )
3 1 2 eqtrd 
 |-  ( ph -> A = C )
4 3 eqcomd 
 |-  ( ph -> C = A )