Theorem imbi2 314

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 307	1 |- ((ph <-> ps) -> ((ch -> ph) <-> (ch -> ps)))

Syntax hints:   -> wi 4   <-> wb 176

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 177

This theorem is referenced by:  3impexpbicom  1367