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Metamath Proof Explorer

Theorem eqtr2d

Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999)

Ref Expression
Hypotheses eqtr2d.1 ⊢ φ → A = B
eqtr2d.2 ⊢ φ → B = C
Assertion eqtr2d ⊢ φ → C = A

Proof

Step Hyp Ref Expression
1 eqtr2d.1 ⊢ φ → A = B
2 eqtr2d.2 ⊢ φ → B = C
3 1 2 eqtrd ⊢ φ → A = C
4 3 eqcomd ⊢ φ → C = A