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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 2432 with a disjoint variable condition, which does not require ax-13 2370. (Contributed by Mario Carneiro, 11-Aug-2016.) Avoid ax-13 2370. (Revised by Gino Giotto, 10-Jan-2024.) (Proof shortened by Wolf Lammen, 25-Sep-2024.) |
Ref | Expression |
---|---|
nfnaew | ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbnaev 2064 | . 2 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) | |
2 | 1 | nf5i 2141 | 1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1538 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 1912 ax-6 1970 ax-7 2010 ax-10 2136 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1781 df-nf 1785 |
This theorem is referenced by: nfriotadw 7301 |
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