Theorem necon3aiOLD 2970

Description: Obsolete version of necon3ai 2969 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.)

Hypothesis

Ref	Expression
necon3ai.1	⊢ (𝜑 → 𝐴 = 𝐵)

Assertion

Ref	Expression
necon3aiOLD	⊢ (𝐴 ≠ 𝐵 → ¬ 𝜑)

Proof of Theorem necon3aiOLD

Step	Hyp	Ref	Expression
1		necon3ai.1	. . 3 ⊢ (𝜑 → 𝐴 = 𝐵)
2		nne 2948	. . 3 ⊢ (¬ 𝐴 ≠ 𝐵 ↔ 𝐴 = 𝐵)
3	1, 2	sylibr 233	. 2 ⊢ (𝜑 → ¬ 𝐴 ≠ 𝐵)
4	3	con2i 139	1 ⊢ (𝐴 ≠ 𝐵 → ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1541   ≠ wne 2944

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-ne 2945

This theorem is referenced by: (None)