Theorem syl6d 75

Description: A nested syllogism deduction. Deduction associated with syl6 35. (Contributed by NM, 11-May-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by Mel L. O'Cat, 2-Feb-2006.)

Hypotheses

Ref	Expression
syl6d.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
syl6d.2	|- ( ph -> ( th -> ta ) )

Assertion

Ref	Expression
syl6d	|- ( ph -> ( ps -> ( ch -> ta ) ) )

Proof of Theorem syl6d

Step	Hyp	Ref	Expression
1		syl6d.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		syl6d.2	. . 3 |- ( ph -> ( th -> ta ) )
3	2	a1d 25	. 2 |- ( ph -> ( ps -> ( th -> ta ) ) )
4	1, 3	syldd 72	1 |- ( ph -> ( ps -> ( ch -> 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:  syl8  76  sbi1  2392  omlimcl  7658  ltexprlem7  9864  axpre-sup  9990  caubnd  14098  ubthlem1  27726  poimirlem29  33438  ee13  38710  ssralv2  38737  rspsbc2  38744  truniALT  38751  stgoldbwt  41664