Theorem falnorfalOLD 1594

Description: Obsolete version of falnorfal 1593 as of 17-Dec-2023. (Contributed by Remi, 25-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem falnorfalOLD

Step	Hyp	Ref	Expression
1		df-nor 1523	. 2 ⊢ ((⊥ ⊽ ⊥) ↔ ¬ (⊥ ∨ ⊥))
2		notfal 1567	. . . . 5 ⊢ (¬ ⊥ ↔ ⊤)
3	2	bicomi 223	. . . 4 ⊢ (⊤ ↔ ¬ ⊥)
4		falorfal 1579	. . . . 5 ⊢ ((⊥ ∨ ⊥) ↔ ⊥)
5	4	bicomi 223	. . . 4 ⊢ (⊥ ↔ (⊥ ∨ ⊥))
6	3, 5	xchbinx 333	. . 3 ⊢ (⊤ ↔ ¬ (⊥ ∨ ⊥))
7	6	bicomi 223	. 2 ⊢ (¬ (⊥ ∨ ⊥) ↔ ⊤)
8	1, 7	bitri 274	1 ⊢ ((⊥ ⊽ ⊥) ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 205   ∨ wo 843   ⊽ wnor 1522  ⊤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 844  df-nor 1523  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)