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Metamath Proof Explorer

Theorem eqtr3d

Description: An equality transitivity equality deduction. (Contributed by NM, 18-Jul-1995)

Ref Expression
Hypotheses eqtr3d.1 
|- ( ph -> A = B )
eqtr3d.2 
|- ( ph -> A = C )
Assertion eqtr3d 
|- ( ph -> B = C )

Proof

Step Hyp Ref Expression
1 eqtr3d.1 
 |-  ( ph -> A = B )
2 eqtr3d.2 
 |-  ( ph -> A = C )
3 1 eqcomd 
 |-  ( ph -> B = A )
4 3 2 eqtrd 
 |-  ( ph -> B = C )