Theorem pm5.501 356

Description: Theorem *5.501 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.501	|- ( ph -> ( ps <-> ( ph <-> ps ) ) )

Proof of Theorem pm5.501

Step	Hyp	Ref	Expression
1		pm5.1im 253	. 2 |- ( ph -> ( ps -> ( ph <-> ps ) ) )
2		biimp 205	. . 3 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
3	2	com12 32	. 2 |- ( ph -> ( ( ph <-> ps ) -> ps ) )
4	1, 3	impbid 202	1 |- ( ph -> ( ps <-> ( ph <-> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196

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

This theorem is referenced by:  ibib  357  ibibr  358  nbn2  360  pm5.18  371  biass  374  pm5.1  902  sadadd2lem2  15172  isclo  20891  nrmmetd  22379  bj-bibibi  32571