Theorem pm5.74d 238

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		pm5.74 235	. 2 |- ((ps -> (ch <-> th)) <-> ((ps -> ch) <-> (ps -> th)))
3	1, 2	sylib 188	1 |- (ph -> ((ps -> ch) <-> (ps -> th)))

Syntax hints:   -> wi 4   <-> wb 176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  imbi2d  307  imim21b  356  pm5.74da  668  2mos  2283  dfiin2g  4001