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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 2433 with a disjoint variable condition, which does not require ax-13 2371. (Contributed by Mario Carneiro, 11-Aug-2016.) (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 2070 | . 2 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) | |
2 | 1 | nf5i 2148 | 1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1541 Ⅎwnf 1791 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2018 ax-10 2143 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1788 df-nf 1792 |
This theorem is referenced by: nfriotadw 7156 |
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