Theorem syl5d 53

Description: A nested syllogism deduction. (The proof was shortened by Josh Purinton, 29-Dec-00.)

Hypotheses

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

Assertion

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

Proof of Theorem syl5d

Step	Hyp	Ref	Expression
1		syl5d.1	. 2 |- (ph -> (ps -> (ch -> th)))
2		syl5d.2	. . 3 |- (ph -> (ta -> ch))
3	2	syl4d 28	. 2 |- (ph -> ((ch -> th) -> (ta -> th)))
4	1, 3	syld 27	1 |- (ph -> (ps -> (ta -> th)))

Syntax hints:   -> wi 2

This theorem is referenced by:  syl9 55  sbi1 884  isofrlem 2939  nnmordi 3188  kmlem8 3587  sqrlem6 4736

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

metamath.org