Theorem syl5d 68

Description: A nested syllogism deduction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by O'Cat, 2-Feb-2006.)

Hypotheses

Ref	Expression
syl5d.1	|- ( ph -> ( ps -> ch ) )
syl5d.2	|- ( ph -> ( th -> ( ch -> ta ) ) )

Assertion

Ref	Expression
syl5d	|- ( ph -> ( th -> ( ps -> ta ) ) )

Proof of Theorem syl5d

Step	Hyp	Ref	Expression
1		syl5d.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	a1d 22	. 2 |- ( ph -> ( th -> ( ps -> ch ) ) )
3		syl5d.2	. 2 |- ( ph -> ( th -> ( ch -> ta ) ) )
4	2, 3	syldd 67	1 |- ( ph -> ( th -> ( ps -> ta ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  syl7  69  syl9  72  imim12d  74  jaddc  865  pm4.79dc  904  rnglidlmcl  14036