Theorem pm5.74da 447

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 4-May-2007.)

Hypothesis

Ref	Expression
pm5.74da.1	|- ( ( ph /\ ps ) -> ( ch <-> th ) )

Assertion

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

Proof of Theorem pm5.74da

Step	Hyp	Ref	Expression
1		pm5.74da.1	. . 3 |- ( ( ph /\ ps ) -> ( ch <-> th ) )
2	1	ex 115	. 2 |- ( ph -> ( ps -> ( ch <-> th ) ) )
3	2	pm5.74d 182	1 |- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  cbvaldvaw  1986  ralbida  2544  elrab3t  2981  dff13  5974  omniwomnimkv  7507  fsumparts  12237  isprm3  12896  cnntr  15326  metcnp  15613  limcdifap  15763