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Mirrors > Home > ILE Home > Th. List > neii | GIF version |
Description: Inference associated with df-ne 2206. (Contributed by BJ, 7-Jul-2018.) |
Ref | Expression |
---|---|
neii.1 | ⊢ 𝐴 ≠ 𝐵 |
Ref | Expression |
---|---|
neii | ⊢ ¬ 𝐴 = 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neii.1 | . 2 ⊢ 𝐴 ≠ 𝐵 | |
2 | df-ne 2206 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
3 | 1, 2 | mpbi 133 | 1 ⊢ ¬ 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1243 ≠ wne 2204 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 |
This theorem depends on definitions: df-bi 110 df-ne 2206 |
This theorem is referenced by: 2dom 6285 ine0 7391 inelr 7575 xrltnr 8701 pnfnlt 8708 xrlttri3 8718 nltpnft 8730 |
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