Theorem truxorfal 1585

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 1511	. . 3 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ (⊤ ↔ ⊥))
2		trubifal 1570	. . 3 ⊢ ((⊤ ↔ ⊥) ↔ ⊥)
3	1, 2	xchbinx 334	. 2 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ ⊥)
4		notfal 1567	. 2 ⊢ (¬ ⊥ ↔ ⊤)
5	3, 4	bitri 275	1 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 206   ⊻ wxo 1510  ⊤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 207  df-xor 1511  df-tru 1542  df-fal 1552

This theorem is referenced by:  falxortru  1586