Theorem syl5d 55

Description: A nested syllogism deduction. (The proof was shortened by Josh Purinton, 29-Dec-2000 and shortened further by O'Cat, 2-Feb-2006.)

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.2	. . 3 |- (ph -> (ta -> ch))
2	1	a1d 12	. 2 |- (ph -> (ps -> (ta -> ch)))
3		syl5d.1	. 2 |- (ph -> (ps -> (ch -> th)))
4	2, 3	syldd 50	1 |- (ph -> (ps -> (ta -> th)))

Syntax hints:   -> wi 3

This theorem is referenced by:  syl9 57  sbi1 1230  ralxfrd 2892  tfinds 3156  isofrlem 3892  kmlem9 4753  squeeze0 5880  sqrlem6 6616  bccl2t 6917

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7

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