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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdne | GIF version |
Description: Inequality of two setvars is a bounded formula. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdne | ⊢ BOUNDED 𝑥 ≠ 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bdeq 9940 | . . 3 ⊢ BOUNDED 𝑥 = 𝑦 | |
2 | 1 | ax-bdn 9937 | . 2 ⊢ BOUNDED ¬ 𝑥 = 𝑦 |
3 | df-ne 2206 | . 2 ⊢ (𝑥 ≠ 𝑦 ↔ ¬ 𝑥 = 𝑦) | |
4 | 2, 3 | bd0r 9945 | 1 ⊢ BOUNDED 𝑥 ≠ 𝑦 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ≠ wne 2204 BOUNDED wbd 9932 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-bd0 9933 ax-bdn 9937 ax-bdeq 9940 |
This theorem depends on definitions: df-bi 110 df-ne 2206 |
This theorem is referenced by: (None) |
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