Theorem nalf 32402

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 32401	. 2 ⊢ ∀𝑥 ¬ ⊥
2		falim 1498	. . 3 ⊢ (⊥ → ¬ ∀𝑥 ¬ ⊥)
3	2	sps 2055	. 2 ⊢ (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
4	1, 3	mt2 191	1 ⊢ ¬ ∀𝑥⊥

Syntax hints:  ¬ wn 3  ∀wal 1481  ⊥wfal 1488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-fal 1489  df-ex 1705

This theorem is referenced by: (None)