Theorem tbsyl 32381

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

Hypotheses

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

Assertion

Ref	Expression
tbsyl	|- ( ph -> ch )

Proof of Theorem tbsyl

Step	Hyp	Ref	Expression
1		tbsyl.2	. 2 |- ( ps -> ch )
2		tbsyl.1	. . 3 |- ( ph -> ps )
3		tb-ax1 32378	. . 3 |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )
4	2, 3	ax-mp 5	. 2 |- ( ( ps -> ch ) -> ( ph -> ch ) )
5	1, 4	ax-mp 5	1 |- ( ph -> ch )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  re1ax2lem  32382  re1ax2  32383