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Mirrors > Home > ILE Home > Th. List > neir | GIF version |
Description: Inference associated with df-ne 2348. (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 2348 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
3 | 1, 2 | mpbir 146 | 1 ⊢ 𝐴 ≠ 𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1353 ≠ wne 2347 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-ne 2348 |
This theorem is referenced by: exmidonfinlem 7191 pw1ne1 7227 pw1ne3 7228 sucpw1nel3 7231 ine0 8350 pwle2 14718 |
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