Theorem truxortru 1584

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 1504	. . 3 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ (⊤ ↔ ⊤))
2		trubitru 1568	. . 3 ⊢ ((⊤ ↔ ⊤) ↔ ⊤)
3	1, 2	xchbinx 333	. 2 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ ⊤)
4		nottru 1566	. 2 ⊢ (¬ ⊤ ↔ ⊥)
5	3, 4	bitri 274	1 ⊢ ((⊤ ⊻ ⊤) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 205   ⊻ wxo 1503  ⊤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-xor 1504  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)