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Metamath Proof Explorer

Theorem 3eqtr4g

Description: A chained equality inference, useful for converting to definitions. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses 3eqtr4g.1 
|- ( ph -> A = B )
3eqtr4g.2 
|- C = A
3eqtr4g.3 
|- D = B
Assertion 3eqtr4g 
|- ( ph -> C = D )

Proof

Step Hyp Ref Expression
1 3eqtr4g.1 
 |-  ( ph -> A = B )
2 3eqtr4g.2 
 |-  C = A
3 3eqtr4g.3 
 |-  D = B
4 2 1 eqtrid 
 |-  ( ph -> C = B )
5 4 3 eqtr4di 
 |-  ( ph -> C = D )