Theorem falnorfalOLD 1592

Description: Obsolete version of falnorfal 1591 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 1521	. 2 ⊢ ((⊥ ⊽ ⊥) ↔ ¬ (⊥ ∨ ⊥))
2		notfal 1565	. . . . 5 ⊢ (¬ ⊥ ↔ ⊤)
3	2	bicomi 226	. . . 4 ⊢ (⊤ ↔ ¬ ⊥)
4		falorfal 1577	. . . . 5 ⊢ ((⊥ ∨ ⊥) ↔ ⊥)
5	4	bicomi 226	. . . 4 ⊢ (⊥ ↔ (⊥ ∨ ⊥))
6	3, 5	xchbinx 336	. . 3 ⊢ (⊤ ↔ ¬ (⊥ ∨ ⊥))
7	6	bicomi 226	. 2 ⊢ (¬ (⊥ ∨ ⊥) ↔ ⊤)
8	1, 7	bitri 277	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-tru 1540  df-fal 1550

This theorem is referenced by: (None)