Theorem syl8 65

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 10	. 2 |- (ph -> (th -> ta))
4	1, 3	syl6d 64	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:  com45  83  syl8ib  222  imp5a  581  3exp  1150  nclenn  6249