Theorem truxortru 1614

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

Assertion

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

Proof of Theorem truxortru

Step	Hyp	Ref	Expression
1		df-xor 1541	. . 3 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ (⊤ ↔ ⊤))
2		trubitru 1598	. . 3 ⊢ ((⊤ ↔ ⊤) ↔ ⊤)
3	1, 2	xchbinx 337	. 2 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ ⊤)
4		nottru 1596	. 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: (None)