Theorem necon2i

Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007)

	Ref	Expression
Hypothesis	necon2i.1	⊢ ( 𝐴 = 𝐵 → 𝐶 ≠ 𝐷 )
Assertion	necon2i	⊢ ( 𝐶 = 𝐷 → 𝐴 ≠ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		necon2i.1	⊢ ( 𝐴 = 𝐵 → 𝐶 ≠ 𝐷 )
2	1	neneqd	⊢ ( 𝐴 = 𝐵 → ¬ 𝐶 = 𝐷 )
3	2	necon2ai	⊢ ( 𝐶 = 𝐷 → 𝐴 ≠ 𝐵 )