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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 2181 in conjunction with distinctors. (Contributed by Wolf Lammen, 2-Sep-2018.) |
Ref | Expression |
---|---|
nfna1 | ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2175 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfn 1931 | 1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1628 Ⅎwnf 1855 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1869 ax-4 1884 ax-10 2166 |
This theorem depends on definitions: df-bi 197 df-or 384 df-ex 1852 df-nf 1857 |
This theorem is referenced by: dvelimhw 2316 nfeqf 2444 equs5 2486 nfsb2 2495 wl-equsb3 33648 wl-sbcom2d-lem1 33653 wl-ax11-lem3 33675 wl-ax11-lem4 33676 wl-ax11-lem6 33678 wl-ax11-lem7 33679 |
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