Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nner | GIF version |
Description: Negation of inequality. (Contributed by Jim Kingdon, 23-Dec-2018.) |
Ref | Expression |
---|---|
nner | ⊢ (𝐴 = 𝐵 → ¬ 𝐴 ≠ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2246 | . . 3 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
2 | 1 | biimpi 118 | . 2 ⊢ (𝐴 ≠ 𝐵 → ¬ 𝐴 = 𝐵) |
3 | 2 | con2i 589 | 1 ⊢ (𝐴 = 𝐵 → ¬ 𝐴 ≠ 𝐵) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 = wceq 1284 ≠ wne 2245 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-in1 576 ax-in2 577 |
This theorem depends on definitions: df-bi 115 df-ne 2246 |
This theorem is referenced by: nn0eln0 4359 funtpg 4970 fin0 6369 |
Copyright terms: Public domain | W3C validator |