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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 ⊢ φ → A = B
3eqtr4g.2 ⊢ C = A
3eqtr4g.3 ⊢ D = B
Assertion 3eqtr4g ⊢ φ → C = D

Proof

Step Hyp Ref Expression
1 3eqtr4g.1 ⊢ φ → A = B
2 3eqtr4g.2 ⊢ C = A
3 3eqtr4g.3 ⊢ D = B
4 2 1 eqtrid ⊢ φ → C = B
5 4 3 eqtr4di ⊢ φ → C = D