Theorem falxortru 1584

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 1504	. 2 ⊢ ((⊥ ⊻ ⊤) ↔ (⊤ ⊻ ⊥))
2		truxorfal 1583	. 2 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤)
3	1, 2	bitri 277	1 ⊢ ((⊥ ⊻ ⊤) ↔ ⊤)

Syntax hints:   ↔ wb 208   ⊻ wxo 1501  ⊤wtru 1538  ⊥wfal 1549

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 1502  df-tru 1540  df-fal 1550

This theorem is referenced by: (None)