Theorem falnorfal 1615

Description: A ⊽ identity. (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 17-Dec-2023.)

Assertion

Ref	Expression
falnorfal	⊢ ((⊥ ⊽ ⊥) ↔ ⊤)

Proof of Theorem falnorfal

Step	Hyp	Ref	Expression
1		df-nor 1552	. . 3 ⊢ ((⊥ ⊽ ⊥) ↔ ¬ (⊥ ∨ ⊥))
2		falorfal 1603	. . 3 ⊢ ((⊥ ∨ ⊥) ↔ ⊥)
3	1, 2	xchbinx 337	. 2 ⊢ ((⊥ ⊽ ⊥) ↔ ¬ ⊥)
4		notfal 1591	. 2 ⊢ (¬ ⊥ ↔ ⊤)
5	3, 4	bitri 278	1 ⊢ ((⊥ ⊽ ⊥) ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 209   ∨ wo 860   ⊽ wnor 1551  ⊤wtru 1564  ⊥wfal 1575

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-or 861  df-nor 1552  df-tru 1566  df-fal 1576

This theorem is referenced by: (None)