Metamath Proof Explorer


Theorem eqtr4di

Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses eqtr4di.1 ( 𝜑𝐴 = 𝐵 )
eqtr4di.2 𝐶 = 𝐵
Assertion eqtr4di ( 𝜑𝐴 = 𝐶 )

Proof

Step Hyp Ref Expression
1 eqtr4di.1 ( 𝜑𝐴 = 𝐵 )
2 eqtr4di.2 𝐶 = 𝐵
3 2 eqcomi 𝐵 = 𝐶
4 1 3 eqtrdi ( 𝜑𝐴 = 𝐶 )