Theorem pm5.74ri 261

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

Hypothesis

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

Assertion

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

Proof of Theorem pm5.74ri

Step	Hyp	Ref	Expression
1		pm5.74ri.1	. 2 |- ( ( ph -> ps ) <-> ( ph -> ch ) )
2		pm5.74 259	. 2 |- ( ( ph -> ( ps <-> ch ) ) <-> ( ( ph -> ps ) <-> ( ph -> ch ) ) )
3	1, 2	mpbir 221	1 |- ( ph -> ( ps <-> ch ) )

Syntax hints:   -> wi 4   <-> wb 196

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 197

This theorem is referenced by:  bitrd  268  bibi2d  332  tbt  359  cbval2  2279  cbvaldva  2281  sbied  2409  sbco2d  2416  axgroth6  9650  isprm2  15395  ufileu  21723  bj-cbval2v  32737