Theorem trunortruOLD 1586

Description: Obsolete version of trunortru 1585 as of 7-Dec-2023. (Contributed by Remi, 25-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem trunortruOLD

Step	Hyp	Ref	Expression
1		df-nor 1520	. 2 ⊢ ((⊤ ⊽ ⊤) ↔ ¬ (⊤ ∨ ⊤))
2		tru 1540	. . . . 5 ⊢ ⊤
3	2	orci 861	. . . 4 ⊢ (⊤ ∨ ⊤)
4	3	notnoti 145	. . 3 ⊢ ¬ ¬ (⊤ ∨ ⊤)
5	4	bifal 1552	. 2 ⊢ (¬ (⊤ ∨ ⊤) ↔ ⊥)
6	1, 5	bitri 277	1 ⊢ ((⊤ ⊽ ⊤) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 208   ∨ wo 843   ⊽ wnor 1519  ⊤wtru 1537  ⊥wfal 1548

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 1520  df-tru 1539  df-fal 1549

This theorem is referenced by: (None)