Theorem imbi2 226

Description: Theorem *4.85 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.)

Assertion

Ref	Expression
imbi2	|- ( ( ph <-> ps ) -> ( ( ch -> ph ) <-> ( ch -> ps ) ) )

Proof of Theorem imbi2

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph <-> ps ) -> ( ph <-> ps ) )
2	1	imbi2d 219	1 |- ( ( ph <-> ps ) -> ( ( ch -> ph ) <-> ( ch -> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  3impexpbicom  1327