Theorem falxorfal 1361

Description: A ⊻ identity. (Contributed by David A. Wheeler, 9-May-2015.)

Assertion

Ref	Expression
falxorfal	⊢ (( ⊥ ⊻ ⊥ ) ↔ ⊥ )

Proof of Theorem falxorfal

Step	Hyp	Ref	Expression
1		df-xor 1305	. . 3 ⊢ (( ⊥ ⊻ ⊥ ) ↔ ¬ ( ⊥ ↔ ⊥ ))
2		falbifal 1353	. . 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)