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 φ A = B
3eqtr3g.2 A = C
3eqtr3g.3 B = D
Assertion 3eqtr3g φ C = D

Proof

Step Hyp Ref Expression
1 3eqtr3g.1 φ A = B
2 3eqtr3g.2 A = C
3 3eqtr3g.3 B = D
4 2 1 eqtr3id φ C = B
5 4 3 eqtrdi φ C = D