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Metamath Proof Explorer

Theorem eqtr3d

Description: An equality transitivity equality deduction. (Contributed by NM, 18-Jul-1995)

Ref Expression
Hypotheses eqtr3d.1 ⊢ φ → A = B
eqtr3d.2 ⊢ φ → A = C
Assertion eqtr3d ⊢ φ → B = C

Proof

Step Hyp Ref Expression
1 eqtr3d.1 ⊢ φ → A = B
2 eqtr3d.2 ⊢ φ → A = C
3 1 eqcomd ⊢ φ → B = A
4 3 2 eqtrd ⊢ φ → B = C