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Mirrors > Home > ILE Home > Th. List > ax6b | GIF version |
Description: Quantified Negation.
Axiom C5-2 of [Monk2] p. 113.
(Contributed by GD, 27-Jan-2018.) |
Ref | Expression |
---|---|
ax6b | ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-ial 1515 | . 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) | |
2 | 1 | ax6blem 1629 | 1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1330 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-5 1424 ax-gen 1426 ax-ie2 1471 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 |
This theorem is referenced by: hbn1 1631 hbnt 1632 |
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