Metamath Proof Explorer


Theorem 3eqtr3g

Description: A chained equality inference, useful for converting from definitions. (Contributed by NM, 15-Nov-1994)

Ref Expression
Hypotheses 3eqtr3g.1
|- ( ph -> A = B )
3eqtr3g.2
|- A = C
3eqtr3g.3
|- B = D
Assertion 3eqtr3g
|- ( ph -> C = D )

Proof

Step Hyp Ref Expression
1 3eqtr3g.1
 |-  ( ph -> A = B )
2 3eqtr3g.2
 |-  A = C
3 3eqtr3g.3
 |-  B = D
4 2 1 syl5eqr
 |-  ( ph -> C = B )
5 4 3 eqtrdi
 |-  ( ph -> C = D )