Theorem falxortru 1610

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 1537	. 2 ⊢ ((⊥ ⊻ ⊤) ↔ (⊤ ⊻ ⊥))
2		truxorfal 1609	. 2 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤)
3	1, 2	bitri 278	1 ⊢ ((⊥ ⊻ ⊤) ↔ ⊤)

Syntax hints:   ↔ wb 209   ⊻ wxo 1534  ⊤wtru 1564  ⊥wfal 1575

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 210  df-xor 1535  df-tru 1566  df-fal 1576

This theorem is referenced by: (None)