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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 2147 in conjunction with distinctors. (Contributed by Wolf Lammen, 2-Sep-2018.) |
Ref | Expression |
---|---|
nfna1 | ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2141 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfn 1853 | 1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1532 Ⅎwnf 1778 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-10 2130 |
This theorem depends on definitions: df-bi 206 df-or 846 df-ex 1775 df-nf 1779 |
This theorem is referenced by: dvelimhw 2336 nfeqf 2375 equs5 2454 sb4b 2469 nfsb2 2477 ab0OLD 4380 wl-equsb3 37251 wl-sbcom2d-lem1 37254 wl-euequf 37269 wl-ax11-lem3 37282 wl-ax11-lem4 37283 wl-ax11-lem6 37285 wl-ax11-lem7 37286 |
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