Theorem pm5.74rd 172

Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 19-Mar-1997.)

Hypothesis

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

Assertion

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

Proof of Theorem pm5.74rd

Step	Hyp	Ref	Expression
1		pm5.74rd.1	. 2 |- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )
2		pm5.74 168	. 2 |- ( ( ps -> ( ch <-> th ) ) <-> ( ( ps -> ch ) <-> ( ps -> th ) ) )
3	1, 2	sylibr 137	1 |- ( ph -> ( ps -> ( ch <-> th ) ) )

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:  pm5.35  826