Theorem syl6req

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

	Ref	Expression
Hypotheses	syl6req.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	syl6req.2	⊢ 𝐵 = 𝐶
Assertion	syl6req	⊢ ( 𝜑 → 𝐶 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		syl6req.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		syl6req.2	⊢ 𝐵 = 𝐶
3	1 2	syl6eq	⊢ ( 𝜑 → 𝐴 = 𝐶 )
4	3	eqcomd	⊢ ( 𝜑 → 𝐶 = 𝐴 )