Theorem neeqtri

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012)

	Ref	Expression
Hypotheses	neeqtr.1	⊢ 𝐴 ≠ 𝐵
	neeqtr.2	⊢ 𝐵 = 𝐶
Assertion	neeqtri	⊢ 𝐴 ≠ 𝐶

Proof

Step	Hyp	Ref	Expression
1		neeqtr.1	⊢ 𝐴 ≠ 𝐵
2		neeqtr.2	⊢ 𝐵 = 𝐶
3	2	neeq2i	⊢ ( 𝐴 ≠ 𝐵 ↔ 𝐴 ≠ 𝐶 )
4	1 3	mpbi	⊢ 𝐴 ≠ 𝐶