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Metamath Proof Explorer

Theorem eqtr2id

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998)

Ref Expression
Hypotheses eqtr2id.1 ⊢ A = B
eqtr2id.2 ⊢ φ → B = C
Assertion eqtr2id ⊢ φ → C = A

Proof

Step Hyp Ref Expression
1 eqtr2id.1 ⊢ A = B
2 eqtr2id.2 ⊢ φ → B = C
3 1 2 eqtrid ⊢ φ → A = C
4 3 eqcomd ⊢ φ → C = A