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Mirrors > Home > MPE Home > Th. List > nfna1 | Structured version Visualization version GIF version |
Description: A convenience theorem particularly designed to remove dependencies on ax-11 2093 in conjunction with distinctors. (Contributed by Wolf Lammen, 2-Sep-2018.) |
Ref | Expression |
---|---|
nfna1 | ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2088 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfn 1819 | 1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1505 Ⅎwnf 1746 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-10 2079 |
This theorem depends on definitions: df-bi 199 df-or 834 df-ex 1743 df-nf 1747 |
This theorem is referenced by: dvelimhw 2279 nfeqf 2311 equs5 2397 nfsb2 2443 nfsb2ALT 2527 wl-equsb3 34233 wl-sbcom2d-lem1 34236 wl-euequf 34251 wl-ax11-lem3 34260 wl-ax11-lem4 34261 wl-ax11-lem6 34263 wl-ax11-lem7 34264 |
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