Theorem falxorfal 1522

Description: A ⊻ identity. (Contributed by David A. Wheeler, 9-May-2015.)

Assertion

Ref	Expression
falxorfal	⊢ ((⊥ ⊻ ⊥) ↔ ⊥)

Proof of Theorem falxorfal

Step	Hyp	Ref	Expression
1		df-xor 1457	. . 3 ⊢ ((⊥ ⊻ ⊥) ↔ ¬ (⊥ ↔ ⊥))
2		falbifal 1514	. . 3 ⊢ ((⊥ ↔ ⊥) ↔ ⊤)
3	1, 2	xchbinx 323	. 2 ⊢ ((⊥ ⊻ ⊥) ↔ ¬ ⊤)
4		nottru 1509	. 2 ⊢ (¬ ⊤ ↔ ⊥)
5	3, 4	bitri 263	1 ⊢ ((⊥ ⊻ ⊥) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 195   ⊻ wxo 1456  ⊤wtru 1476  ⊥wfal 1480

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 196  df-xor 1457  df-tru 1478  df-fal 1481

This theorem is referenced by: (None)