Theorem imbi1 321

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 315	1 |- ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 184

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 185

This theorem is referenced by:  imbi1i  323  wl-nanbi1  31327  wl-nanbi2  31328  ifpbi1  35548  3impexpVD  36666  ancomstVD  36676  onfrALTVD  36702  hbimpgVD  36715  hbexgVD  36717  ax6e2ndeqVD  36720  ax6e2ndeqALT  36742