Theorem pm5.74d 182

Description: Distribution of implication over biconditional (deduction form). (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		pm5.74 179	. 2 |- ( ( ps -> ( ch <-> th ) ) <-> ( ( ps -> ch ) <-> ( ps -> th ) ) )
3	1, 2	sylib 122	1 |- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )

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:  imbi2d  230  imim21b  253  pm5.74da  443  cbval2  1936  dfiin2g  3949  brecop  6684  dom2lem  6831  nn0ind-raph  9443