Theorem syl5eq

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

	Ref	Expression
Hypotheses	syl5eq.1	⊢ 𝐴 = 𝐵
	syl5eq.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
Assertion	syl5eq	⊢ ( 𝜑 → 𝐴 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		syl5eq.1	⊢ 𝐴 = 𝐵
2		syl5eq.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
3	1	a1i	⊢ ( 𝜑 → 𝐴 = 𝐵 )
4	3 2	eqtrd	⊢ ( 𝜑 → 𝐴 = 𝐶 )