Theorem nbi2 936

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 372	. 2 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )
2		pm5.17 932	. 2 |- ( ( ( ph \/ ps ) /\ -. ( ph /\ ps ) ) <-> ( ph <-> -. ps ) )
3	1, 2	bitr4i 267	1 |- ( -. ( ph <-> ps ) <-> ( ( ph \/ ps ) /\ -. ( ph /\ ps ) ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383   /\ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by:  xor2  1470