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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > hbnae-o | 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). Version of hbnae 2425 using ax-c11 38489. (Contributed by NM, 13-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
hbnae-o | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbae-o 38505 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
2 | 1 | hbn 2284 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-10 2129 ax-11 2146 ax-12 2166 ax-c5 38485 ax-c4 38486 ax-c7 38487 ax-c10 38488 ax-c11 38489 ax-c9 38492 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-ex 1774 df-nf 1778 |
This theorem is referenced by: dvelimf-o 38531 ax12indalem 38547 ax12inda2ALT 38548 |
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