Metamath Proof Explorer


Theorem eqtr2di

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

Ref Expression
Hypotheses eqtr2di.1 ( 𝜑𝐴 = 𝐵 )
eqtr2di.2 𝐵 = 𝐶
Assertion eqtr2di ( 𝜑𝐶 = 𝐴 )

Proof

Step Hyp Ref Expression
1 eqtr2di.1 ( 𝜑𝐴 = 𝐵 )
2 eqtr2di.2 𝐵 = 𝐶
3 1 2 eqtrdi ( 𝜑𝐴 = 𝐶 )
4 3 eqcomd ( 𝜑𝐶 = 𝐴 )