Theorem dfbi3OLD 995

Description: Obsolete proof of dfbi3 994 as of 29-Oct-2021. (Contributed by NM, 27-Jun-2002.) (Proof shortened by Wolf Lammen, 3-Nov-2013.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
dfbi3OLD	|- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) )

Proof of Theorem dfbi3OLD

Step	Hyp	Ref	Expression
1		xor 935	. 2 |- ( -. ( ph <-> -. ps ) <-> ( ( ph /\ -. -. ps ) \/ ( -. ps /\ -. ph ) ) )
2		pm5.18 371	. 2 |- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
3		notnotb 304	. . . 4 |- ( ps <-> -. -. ps )
4	3	anbi2i 730	. . 3 |- ( ( ph /\ ps ) <-> ( ph /\ -. -. ps ) )
5		ancom 466	. . 3 |- ( ( -. ph /\ -. ps ) <-> ( -. ps /\ -. ph ) )
6	4, 5	orbi12i 543	. 2 |- ( ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) <-> ( ( ph /\ -. -. ps ) \/ ( -. ps /\ -. ph ) ) )
7	1, 2, 6	3bitr4i 292	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: (None)