Metamath Proof Explorer


Theorem necon2bi

Description: Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007)

Ref Expression
Hypothesis necon2bi.1 ( 𝜑𝐴𝐵 )
Assertion necon2bi ( 𝐴 = 𝐵 → ¬ 𝜑 )

Proof

Step Hyp Ref Expression
1 necon2bi.1 ( 𝜑𝐴𝐵 )
2 1 neneqd ( 𝜑 → ¬ 𝐴 = 𝐵 )
3 2 con2i ( 𝐴 = 𝐵 → ¬ 𝜑 )