Theorem trunortru 1586

Description: A ⊽ identity. (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 7-Dec-2023.)

Assertion

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

Proof of Theorem trunortru

Step	Hyp	Ref	Expression
1		df-nor 1521	. . 3 ⊢ ((⊤ ⊽ ⊤) ↔ ¬ (⊤ ∨ ⊤))
2		truortru 1574	. . 3 ⊢ ((⊤ ∨ ⊤) ↔ ⊤)
3	1, 2	xchbinx 336	. 2 ⊢ ((⊤ ⊽ ⊤) ↔ ¬ ⊤)
4		df-fal 1550	. 2 ⊢ (⊥ ↔ ¬ ⊤)
5	3, 4	bitr4i 280	1 ⊢ ((⊤ ⊽ ⊤) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 208   ∨ wo 843   ⊽ wnor 1520  ⊤wtru 1538  ⊥wfal 1549

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 209  df-or 844  df-nor 1521  df-fal 1550

This theorem is referenced by: (None)