Theorem nalfal

Description: Not all sets hold F. as true. (Contributed by Anthony Hart, 13-Sep-2011)

	Ref	Expression
Assertion	nalfal	⊢ ¬ ∀ 𝑥 ⊥

Proof

Step	Hyp	Ref	Expression
1		alfal	⊢ ∀ 𝑥 ¬ ⊥
2		falim	⊢ ( ⊥ → ¬ ∀ 𝑥 ¬ ⊥ )
3	2	sps	⊢ ( ∀ 𝑥 ⊥ → ¬ ∀ 𝑥 ¬ ⊥ )
4	1 3	mt2	⊢ ¬ ∀ 𝑥 ⊥