Theorem trunorfal 1618

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

Assertion

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

Proof of Theorem trunorfal

Step	Hyp	Ref	Expression
1		df-nor 1557	. . 3 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ (⊤ ∨ ⊥))
2		truorfal 1606	. . 3 ⊢ ((⊤ ∨ ⊥) ↔ ⊤)
3	1, 2	xchbinx 337	. 2 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ ⊤)
4		df-fal 1581	. 2 ⊢ (⊥ ↔ ¬ ⊤)
5	3, 4	bitr4i 281	1 ⊢ ((⊤ ⊽ ⊥) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 209   ∨ wo 860   ⊽ wnor 1556  ⊤wtru 1569  ⊥wfal 1580

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 1557  df-tru 1571  df-fal 1581

This theorem is referenced by:  falnortru  1619