Theorem nbi2 862

Description: Two ways to express "exclusive or." (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Jan-2013.)

Assertion

Ref	Expression
nbi2	|- (-. (ph <-> ps) <-> ((ph \/ ps) /\ -. (ph /\ ps)))

Proof of Theorem nbi2

Step	Hyp	Ref	Expression
1		xor3 346	. 2 |- (-. (ph <-> ps) <-> (ph <-> -. ps))
2		pm5.17 858	. 2 |- (((ph \/ ps) /\ -. (ph /\ ps)) <-> (ph <-> -. ps))
3	1, 2	bitr4i 243	1 |- (-. (ph <-> ps) <-> ((ph \/ ps) /\ -. (ph /\ ps)))

This proof depends on syntax axioms:  -. wn 3   <-> wb 176   \/ wo 357   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is used by:  xor2  1310