Theorem necon3aiOLD

Description: Obsolete version of necon3ai as of 28-Oct-2024. (Contributed by NM, 23-May-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	necon3ai.1	$$⊢\phi \to A=B$$
Assertion	necon3aiOLD	$$⊢A\ne B\to \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		necon3ai.1	$$⊢\phi \to A=B$$
2		nne	$$⊢\neg A\ne B\leftrightarrow A=B$$
3	1 2	sylibr	$$⊢\phi \to \neg A\ne B$$
4	3	con2i	$$⊢A\ne B\to \neg \phi$$