Theorem pm3.33 609

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 83	. 2 |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )
2	1	imp 445	1 |- ( ( ( ph -> ps ) /\ ( ps -> ch ) ) -> ( ph -> ch ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  alsyl  1820  ucncn  22089  bnj1023  30851  bnj907  31035  2sb5ndALT  39168