Theorem falxortru 1586

Description: A ⊻ identity. (Contributed by David A. Wheeler, 9-May-2015.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)

Assertion

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

Proof of Theorem falxortru

Step	Hyp	Ref	Expression
1		xorcom 1509	. 2 ⊢ ((⊥ ⊻ ⊤) ↔ (⊤ ⊻ ⊥))
2		truxorfal 1585	. 2 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤)
3	1, 2	bitri 274	1 ⊢ ((⊥ ⊻ ⊤) ↔ ⊤)

Syntax hints:   ↔ wb 205   ⊻ wxo 1506  ⊤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 1507  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)