Theorem pm3.33 343

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 76	. 2 |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )
2	1	imp 123	1 |- ( ( ( ph -> ps ) /\ ( ps -> ch ) ) -> ( ph -> ch ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem is referenced by:  alsyl  1623  sbequilem  1826