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