Theorem imbi1 235

Description: Theorem *4.84 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
imbi1	|- ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )

Proof of Theorem imbi1

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph <-> ps ) -> ( ph <-> ps ) )
2	1	imbi1d 230	1 |- ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  imbi1i  237