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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-naevhba1v | Structured version Visualization version GIF version |
Description: An instance of hbn1w 1997 applied to equality. (Contributed by Wolf Lammen, 7-Apr-2021.) |
Ref | Expression |
---|---|
wl-naevhba1v | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑥 ¬ ∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equequ1 1982 | . 2 ⊢ (𝑥 = 𝑧 → (𝑥 = 𝑦 ↔ 𝑧 = 𝑦)) | |
2 | 1 | hbn1w 1997 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑥 ¬ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1505 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 |
This theorem depends on definitions: df-bi 199 df-an 388 df-ex 1743 |
This theorem is referenced by: (None) |
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