Theorem nalf 31572

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

Assertion

Ref	Expression
nalf	⊢ ¬ ∀𝑥⊥

Proof of Theorem nalf

Step	Hyp	Ref	Expression
1		alnof 31571	. 2 ⊢ ∀𝑥 ¬ ⊥
2		falim 1489	. . 3 ⊢ (⊥ → ¬ ∀𝑥 ¬ ⊥)
3	2	sps 2043	. 2 ⊢ (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
4	1, 3	mt2 190	1 ⊢ ¬ ∀𝑥⊥

Syntax hints:  ¬ wn 3  ∀wal 1473  ⊥wfal 1480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-tru 1478  df-fal 1481  df-ex 1696

This theorem is referenced by: (None)