Theorem trunorfal 1589

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 1526	. . 3 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ (⊤ ∨ ⊥))
2		truorfal 1577	. . 3 ⊢ ((⊤ ∨ ⊥) ↔ ⊤)
3	1, 2	xchbinx 334	. 2 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ ⊤)
4		df-fal 1552	. 2 ⊢ (⊥ ↔ ¬ ⊤)
5	3, 4	bitr4i 277	1 ⊢ ((⊤ ⊽ ⊥) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 205   ∨ wo 844   ⊽ wnor 1525  ⊤wtru 1540  ⊥wfal 1551

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 206  df-or 845  df-nor 1526  df-tru 1542  df-fal 1552

This theorem is referenced by:  falnortru  1591