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Metamath Proof Explorer

Theorem eqtr4d

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

Ref Expression
Hypotheses eqtr4d.1 
|- ( ph -> A = B )
eqtr4d.2 
|- ( ph -> C = B )
Assertion eqtr4d 
|- ( ph -> A = C )

Proof

Step Hyp Ref Expression
1 eqtr4d.1 
 |-  ( ph -> A = B )
2 eqtr4d.2 
 |-  ( ph -> C = B )
3 2 eqcomd 
 |-  ( ph -> B = C )
4 1 3 eqtrd 
 |-  ( ph -> A = C )