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Metamath Proof Explorer

Theorem eqtr4d

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

Ref Expression
Hypotheses eqtr4d.1 ⊢ φ → A = B
eqtr4d.2 ⊢ φ → C = B
Assertion eqtr4d ⊢ φ → A = C

Proof

Step Hyp Ref Expression
1 eqtr4d.1 ⊢ φ → A = B
2 eqtr4d.2 ⊢ φ → C = B
3 2 eqcomd ⊢ φ → B = C
4 1 3 eqtrd ⊢ φ → A = C