Theorem tbsyl

Description: The weak syllogism from Tarski-Bernays'. (Contributed by Anthony Hart, 16-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	tbsyl.1	|- ( ph -> ps )
	tbsyl.2	|- ( ps -> ch )
Assertion	tbsyl	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		tbsyl.1	|- ( ph -> ps )
2		tbsyl.2	|- ( ps -> ch )
3		tb-ax1	|- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )
4	1 3	ax-mp	|- ( ( ps -> ch ) -> ( ph -> ch ) )
5	2 4	ax-mp	|- ( ph -> ch )