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Mirrors > Home > MPE Home > Th. List > hbnae | Structured version Visualization version GIF version |
Description: All variables are effectively bound in a distinct variable specifier. A version with a distinct variable condition based on fewer axioms is hbnaev 2058. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 13-May-1993.) |
Ref | Expression |
---|---|
hbnae | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbae 2445 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
2 | 1 | hbn 2294 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1526 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-10 2136 ax-11 2151 ax-12 2167 ax-13 2381 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 |
This theorem is referenced by: hbnaes 2449 eujustALT 2650 bj-hbnaeb 34040 ax6e2nd 40769 ax6e2ndVD 41119 ax6e2ndeqVD 41120 ax6e2ndALT 41141 ax6e2ndeqALT 41142 |
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