Theorem pm5.501 330

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 229	. 2 |- (ph -> (ps -> (ph <-> ps)))
2		bi1 178	. . 3 |- ((ph <-> ps) -> (ph -> ps))
3	2	com12 27	. 2 |- (ph -> ((ph <-> ps) -> ps))
4	1, 3	impbid 183	1 |- (ph -> (ps <-> (ph <-> ps)))

Syntax hints:   -> wi 4   <-> wb 176

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

This theorem is referenced by:  ibib  331  ibibr  332  nbn2  334  pm5.18  345  biass  348  pm5.1  830