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Metamath Proof Explorer

Theorem 3eqtr3a

Description: A chained equality inference, useful for converting from definitions. (Contributed by Mario Carneiro, 6-Nov-2015)

Ref Expression
Hypotheses 3eqtr3a.1 
|- A = B
3eqtr3a.2 
|- ( ph -> A = C )
3eqtr3a.3 
|- ( ph -> B = D )
Assertion 3eqtr3a 
|- ( ph -> C = D )

Proof

Step Hyp Ref Expression
1 3eqtr3a.1 
 |-  A = B
2 3eqtr3a.2 
 |-  ( ph -> A = C )
3 3eqtr3a.3 
 |-  ( ph -> B = D )
4 1 3 eqtrid 
 |-  ( ph -> A = D )
5 2 4 eqtr3d 
 |-  ( ph -> C = D )