Theorem imbi1 313

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 308	1 |- ((ph <-> ps) -> ((ph -> ch) <-> (ps -> ch)))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  imbi1i  315