Theorem syl5reqr

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

	Ref	Expression
Hypotheses	syl5reqr.1	⊢ 𝐵 = 𝐴
	syl5reqr.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
Assertion	syl5reqr	⊢ ( 𝜑 → 𝐶 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		syl5reqr.1	⊢ 𝐵 = 𝐴
2		syl5reqr.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
3	1	eqcomi	⊢ 𝐴 = 𝐵
4	3 2	syl5req	⊢ ( 𝜑 → 𝐶 = 𝐴 )