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Mirrors > Home > ILE Home > Th. List > neir | GIF version |
Description: Inference associated with df-ne 2246. (Contributed by BJ, 7-Jul-2018.) |
Ref | Expression |
---|---|
neir.1 | ⊢ ¬ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
neir | ⊢ 𝐴 ≠ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neir.1 | . 2 ⊢ ¬ 𝐴 = 𝐵 | |
2 | df-ne 2246 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
3 | 1, 2 | mpbir 144 | 1 ⊢ 𝐴 ≠ 𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1284 ≠ wne 2245 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-ne 2246 |
This theorem is referenced by: ine0 7498 |
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