Theorem pm5.74d 180

Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 21-Mar-1996.)

Hypothesis

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

Assertion

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

Proof of Theorem pm5.74d

Step	Hyp	Ref	Expression
1		pm5.74d.1	. 2 |- ( ph -> ( ps -> ( ch <-> th ) ) )
2		pm5.74 177	. 2 |- ( ( ps -> ( ch <-> th ) ) <-> ( ( ps -> ch ) <-> ( ps -> th ) ) )
3	1, 2	sylib 120	1 |- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )

Syntax hints:   -> wi 4   <-> 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:  imbi2d  228  imim21b  250  pm5.74da  431  cbval2  1837  dfiin2g  3711  brecop  6219  dom2lem  6275  nn0ind-raph  8464