Theorem pm5.74ri 181

Description: Distribution of implication over biconditional (reverse inference form). (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		pm5.74 179	. 2 |- ( ( ph -> ( ps <-> ch ) ) <-> ( ( ph -> ps ) <-> ( ph -> ch ) ) )
3	1, 2	mpbir 146	1 |- ( ph -> ( ps <-> ch ) )

Syntax hints:   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  bitrd  188  bibi2d  232  tbt  247  cbval2  1936  cbvaldvaw  1945  sbco2d  1985  sbco2vd  1986  isprm2  12310