Theorem truxortru 1581

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 1501	. . 3 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ (⊤ ↔ ⊤))
2		trubitru 1565	. . 3 ⊢ ((⊤ ↔ ⊤) ↔ ⊤)
3	1, 2	xchbinx 336	. 2 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ ⊤)
4		nottru 1563	. 2 ⊢ (¬ ⊤ ↔ ⊥)
5	3, 4	bitri 277	1 ⊢ ((⊤ ⊻ ⊤) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 208   ⊻ wxo 1500  ⊤wtru 1537  ⊥wfal 1548

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-xor 1501  df-tru 1539  df-fal 1549

This theorem is referenced by: (None)