Theorem pm3.33 568

Description: Theorem *3.33 (Syll) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.33	|- (((ph -> ps) /\ (ps -> ch)) -> (ph -> ch))

Proof of Theorem pm3.33

Step	Hyp	Ref	Expression
1		imim1 70	. 2 |- ((ph -> ps) -> ((ps -> ch) -> (ph -> ch)))
2	1	imp 418	1 |- (((ph -> ps) /\ (ps -> ch)) -> (ph -> ch))

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  alsyl  1615