Theorem syl8 70

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 3-Aug-2012.)

Hypotheses

Ref	Expression
syl8.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
syl8.2	|- ( th -> ta )

Assertion

Ref	Expression
syl8	|- ( ph -> ( ps -> ( ch -> ta ) ) )

Proof of Theorem syl8

Step	Hyp	Ref	Expression
1		syl8.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		syl8.2	. . 3 |- ( th -> ta )
3	2	a1i 9	. 2 |- ( ph -> ( th -> ta ) )
4	1, 3	syl6d 69	1 |- ( ph -> ( ps -> ( ch -> ta ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  com45  88  syl8ib  164  imp5a  350  con4biddc  792  3exp  1142  suctr  4248  ssorduni  4304  nneneq  6573  qreccl  9127  bj-inf2vnlem2  11866