Theorem pm5.74i 169

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		pm5.74 168	. 2 |- ( ( ph -> ( ps <-> ch ) ) <-> ( ( ph -> ps ) <-> ( ph -> ch ) ) )
3	1, 2	mpbi 133	1 |- ( ( ph -> ps ) <-> ( ph -> ch ) )

Syntax hints:   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  bitrd  177  imbi2i  215  bibi2d  221  ibib  234  ibibr  235  anclb  302  pm5.42  303  ancrb  305  equsalh  1614  equsal  1615  sb6a  1864  ralbiia  2338  raaan  3327