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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 ⊢ φ → A = C
3eqtr3a.3 ⊢ φ → B = D
Assertion 3eqtr3a ⊢ φ → C = D

Proof

Step Hyp Ref Expression
1 3eqtr3a.1 ⊢ A = B
2 3eqtr3a.2 ⊢ φ → A = C
3 3eqtr3a.3 ⊢ φ → B = D
4 1 3 eqtrid ⊢ φ → A = D
5 2 4 eqtr3d ⊢ φ → C = D