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Mirrors > Home > MPE Home > Th. List > nfnaew | Structured version Visualization version GIF version |
Description: All variables are effectively bound in a distinct variable specifier. Version of nfnae 2456 with a disjoint variable condition, which does not require ax-13 2390. (Contributed by Mario Carneiro, 11-Aug-2016.) (Revised by Gino Giotto, 10-Jan-2024.) |
Ref | Expression |
---|---|
nfnaew | ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbaev 2064 | . . 3 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
2 | 1 | nf5i 2150 | . 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦 |
3 | 2 | nfn 1857 | 1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1535 Ⅎwnf 1784 |
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 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1781 df-nf 1785 |
This theorem is referenced by: nfriotadw 7122 |
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