Theorem syl2 17

Description: A closed form of syllogism. Theorem *2.06 of [WhiteheadRussell] p. 100.

Assertion

Ref	Expression
syl2	|- ((ph -> ps) -> ((ps -> ch) -> (ph -> ch)))

Proof of Theorem syl2

Step	Hyp	Ref	Expression
1		syl1 16	. 2 |- ((ps -> ch) -> ((ph -> ps) -> (ph -> ch)))
2	1	com12 13	1 |- ((ph -> ps) -> ((ps -> ch) -> (ph -> ch)))

Syntax hints:   -> wi 2

This theorem is referenced by:  syl4 19  syl4d 28  looinv 77  immo 1043  sstr2 1510  intss 1983  suppsr2 4017

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

metamath.org