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| Mirrors > Home > MPE Home > Th. List > hbnaev | Structured version Visualization version GIF version | ||
| Description: Any variable is free in ¬ ∀𝑥𝑥 = 𝑦, if 𝑥 and 𝑦 are distinct. This condition is dropped in hbnae 2437, at the expense of more axiom dependencies. Instance of naev2 2061. (Contributed by NM, 13-May-1993.) (Revised by Wolf Lammen, 9-Apr-2021.) |
| Ref | Expression |
|---|---|
| hbnaev | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | naev2 2061 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) |
| Colors of variables: wff setvar class |
| Syntax hints: ¬ wn 3 → wi 4 ∀wal 1538 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 |
| This theorem is referenced by: nfnaew 2149 euae 2660 |
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