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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. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). Usage of this theorem is discouraged because it depends on ax-13 2390. Use the weaker hbnaev 2067 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 2453 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
2 | 1 | hbn 2303 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1535 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-11 2161 ax-12 2177 ax-13 2390 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 |
This theorem is referenced by: hbnaes 2457 eujustALT 2657 bj-hbnaeb 34143 ax6e2nd 40912 ax6e2ndVD 41262 ax6e2ndeqVD 41263 ax6e2ndALT 41284 ax6e2ndeqALT 41285 |
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