Theorem falxortru 1587

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 1514	. 2 ⊢ ((⊥ ⊻ ⊤) ↔ (⊤ ⊻ ⊥))
2		truxorfal 1586	. 2 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤)
3	1, 2	bitri 275	1 ⊢ ((⊥ ⊻ ⊤) ↔ ⊤)

Syntax hints:   ↔ wb 206   ⊻ wxo 1511  ⊤wtru 1541  ⊥wfal 1552

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 1512  df-tru 1543  df-fal 1553

This theorem is referenced by: (None)