Theorem trunorfalOLD 1590

Description: Obsolete version of trunorfal 1589 as of 17-Dec-2023. (Contributed by Remi, 25-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem trunorfalOLD

Step	Hyp	Ref	Expression
1		df-nor 1526	. 2 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ (⊤ ∨ ⊥))
2		tru 1543	. . . . 5 ⊢ ⊤
3	2	orci 862	. . . 4 ⊢ (⊤ ∨ ⊥)
4	3	notnoti 143	. . 3 ⊢ ¬ ¬ (⊤ ∨ ⊥)
5	4	bifal 1555	. 2 ⊢ (¬ (⊤ ∨ ⊥) ↔ ⊥)
6	1, 5	bitri 274	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: (None)