Metamath Proof Explorer


Theorem syl6reqr

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

Ref Expression
Hypotheses syl6reqr.1 ( 𝜑𝐴 = 𝐵 )
syl6reqr.2 𝐶 = 𝐵
Assertion syl6reqr ( 𝜑𝐶 = 𝐴 )

Proof

Step Hyp Ref Expression
1 syl6reqr.1 ( 𝜑𝐴 = 𝐵 )
2 syl6reqr.2 𝐶 = 𝐵
3 2 eqcomi 𝐵 = 𝐶
4 1 3 syl6req ( 𝜑𝐶 = 𝐴 )