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| Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). Usage of this theorem is discouraged because it depends on ax-13 2377. Use the weaker hbnaev 2062 when possible. (Contributed by NM, 13-May-1993.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| hbnae | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | hbae 2436 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
| 2 | 1 | hbn 2295 | 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 ax-10 2141 ax-11 2157 ax-12 2177 ax-13 2377 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-nf 1784 | 
| This theorem is referenced by: hbnaes 2440 eujustALT 2572 bj-hbnaeb 36821 ax6e2nd 44578 ax6e2ndVD 44928 ax6e2ndeqVD 44929 ax6e2ndALT 44950 ax6e2ndeqALT 44951 | 
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