Metamath Proof Explorer


Theorem syl6eq

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

Ref Expression
Hypotheses syl6eq.1 ( 𝜑𝐴 = 𝐵 )
syl6eq.2 𝐵 = 𝐶
Assertion syl6eq ( 𝜑𝐴 = 𝐶 )

Proof

Step Hyp Ref Expression
1 syl6eq.1 ( 𝜑𝐴 = 𝐵 )
2 syl6eq.2 𝐵 = 𝐶
3 2 a1i ( 𝜑𝐵 = 𝐶 )
4 1 3 eqtrd ( 𝜑𝐴 = 𝐶 )