Theorem rb-bijust 1514

Description: Justification for rb-imdf 1515. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem rb-bijust

Step	Hyp	Ref	Expression
1		dfbi1 184	. 2 |- ((ph <-> ps) <-> -. ((ph -> ps) -> -. (ps -> ph)))
2		imor 401	. . . 4 |- ((ph -> ps) <-> (-. ph \/ ps))
3		imor 401	. . . . 5 |- ((ps -> ph) <-> (-. ps \/ ph))
4	3	notbii 287	. . . 4 |- (-. (ps -> ph) <-> -. (-. ps \/ ph))
5	2, 4	imbi12i 316	. . 3 |- (((ph -> ps) -> -. (ps -> ph)) <-> ((-. ph \/ ps) -> -. (-. ps \/ ph)))
6	5	notbii 287	. 2 |- (-. ((ph -> ps) -> -. (ps -> ph)) <-> -. ((-. ph \/ ps) -> -. (-. ps \/ ph)))
7		pm4.62 408	. . 3 |- (((-. ph \/ ps) -> -. (-. ps \/ ph)) <-> (-. (-. ph \/ ps) \/ -. (-. ps \/ ph)))
8	7	notbii 287	. 2 |- (-. ((-. ph \/ ps) -> -. (-. ps \/ ph)) <-> -. (-. (-. ph \/ ps) \/ -. (-. ps \/ ph)))
9	1, 6, 8	3bitri 262	1 |- ((ph <-> ps) <-> -. (-. (-. ph \/ ps) \/ -. (-. ps \/ ph)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357

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-or 359

This theorem is referenced by:  rb-imdf  1515