Theorem truxorfal 1615

Description: A ⊻ identity. (Contributed by David A. Wheeler, 8-May-2015.)

Assertion

Ref	Expression
truxorfal	⊢ ((⊤ ⊻ ⊥) ↔ ⊤)

Proof of Theorem truxorfal

Step	Hyp	Ref	Expression
1		df-xor 1541	. . 3 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ (⊤ ↔ ⊥))
2		trubifal 1600	. . 3 ⊢ ((⊤ ↔ ⊥) ↔ ⊥)
3	1, 2	xchbinx 337	. 2 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ ⊥)
4		notfal 1597	. 2 ⊢ (¬ ⊥ ↔ ⊤)
5	3, 4	bitri 278	1 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209   ⊻ wxo 1540  ⊤wtru 1570  ⊥wfal 1581

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-xor 1541  df-tru 1572  df-fal 1582

This theorem is used by:  falxortru  1616