Theorem nalfal 33864

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

Assertion

Ref	Expression
nalfal	⊢ ¬ ∀𝑥⊥

Proof of Theorem nalfal

Step	Hyp	Ref	Expression
1		alfal 1810	. 2 ⊢ ∀𝑥 ¬ ⊥
2		falim 1555	. . 3 ⊢ (⊥ → ¬ ∀𝑥 ¬ ⊥)
3	2	sps 2182	. 2 ⊢ (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
4	1, 3	mt2 203	1 ⊢ ¬ ∀𝑥⊥

Syntax hints:  ¬ wn 3  ∀wal 1536  ⊥wfal 1550

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2175

This theorem depends on definitions:  df-bi 210  df-tru 1541  df-fal 1551  df-ex 1782

This theorem is referenced by: (None)