Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > neqne | GIF version |
Description: From non equality to inequality. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
neqne | ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (¬ 𝐴 = 𝐵 → ¬ 𝐴 = 𝐵) | |
2 | 1 | neqned 2213 | 1 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 = wceq 1243 ≠ wne 2204 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-ne 2206 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |