Theorem pm5.32d 620

Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 29-Oct-1996.)

Hypothesis

Ref	Expression
pm5.32d.1	|- (ph -> (ps -> (ch <-> th)))

Assertion

Ref	Expression
pm5.32d	|- (ph -> ((ps /\ ch) <-> (ps /\ th)))

Proof of Theorem pm5.32d

Step	Hyp	Ref	Expression
1		pm5.32d.1	. 2 |- (ph -> (ps -> (ch <-> th)))
2		pm5.32 617	. 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   /\ wa 358

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  df-an 360

This theorem is referenced by:  pm5.32rd  621  pm5.32da  622  anbi2d  684  cbval2  2004  cbvex2  2005  cores  5085  isoini  5498  mpt2eq123  5662  nmembers1lem3  6271