Theorem pm5.74da 431

Description: Distribution of implication over biconditional (deduction rule). (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 113	. 2 |- ( ph -> ( ps -> ( ch <-> th ) ) )
3	2	pm5.74d 180	1 |- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> 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:  ralbida  2362  elrab3t  2748  dff13  5428  isprm3  10500