Theorem imbi1 337

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 331	1 |- ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )

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:  imbi1i  339  wl-nanbi1  33300  wl-nanbi2  33301  ifpbi1  37822  3impexpVD  39091  ancomstVD  39101  onfrALTVD  39127  hbimpgVD  39140  hbexgVD  39142  ax6e2ndeqVD  39145  ax6e2ndeqALT  39167