Theorem imbi1 325

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 22	. 2 |- ( ( ph <-> ps ) -> ( ph <-> ps ) )
2	1	imbi1d 319	1 |- ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 188

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 189

This theorem is referenced by:  imbi1i  327  wl-nanbi1  31867  wl-nanbi2  31868  ifpbi1  36133  3impexpVD  37262  ancomstVD  37272  onfrALTVD  37298  hbimpgVD  37311  hbexgVD  37313  ax6e2ndeqVD  37316  ax6e2ndeqALT  37338