Theorem truxortru 1358

Description: A ⊻ identity. (Contributed by David A. Wheeler, 8-May-2015.)

Assertion

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

Proof of Theorem truxortru

Step	Hyp	Ref	Expression
1		df-xor 1305	. . 3 ⊢ (( ⊤ ⊻ ⊤ ) ↔ ¬ ( ⊤ ↔ ⊤ ))
2		trubitru 1350	. . 3 ⊢ (( ⊤ ↔ ⊤ ) ↔ ⊤ )
3	1, 2	xchbinx 301	. 2 ⊢ (( ⊤ ⊻ ⊤ ) ↔ ¬ ⊤ )
4		nottru 1348	. 2 ⊢ (¬ ⊤ ↔ ⊥ )
5	3, 4	bitri 240	1 ⊢ (( ⊤ ⊻ ⊤ ) ↔ ⊥ )

Syntax hints:  ¬ wn 3   ↔ wb 176   ⊻ wxo 1304   ⊤ wtru 1316   ⊥ wfal 1317

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 177  df-xor 1305  df-tru 1319  df-fal 1320

This theorem is referenced by: (None)