Theorem pm5.74i 178

Description: Distribution of implication over biconditional (inference rule). (Contributed by NM, 1-Aug-1994.)

Hypothesis

Ref	Expression
pm5.74i.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
pm5.74i	|- ( ( ph -> ps ) <-> ( ph -> ch ) )

Proof of Theorem pm5.74i

Step	Hyp	Ref	Expression
1		pm5.74i.1	. 2 |- ( ph -> ( ps <-> ch ) )
2		pm5.74 177	. 2 |- ( ( ph -> ( ps <-> ch ) ) <-> ( ( ph -> ps ) <-> ( ph -> ch ) ) )
3	1, 2	mpbi 143	1 |- ( ( ph -> ps ) <-> ( ph -> ch ) )

Syntax hints:   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  bitrd  186  imbi2i  224  bibi2d  230  ibib  243  ibibr  244  anclb  312  pm5.42  313  ancrb  315  equsalh  1654  equsal  1655  sb6a  1905  ralbiia  2380  raaan  3347  isprm4  10501