Theorem syldd 50

Description: Nested syllogism deduction.

Hypotheses

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

Assertion

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

Proof of Theorem syldd

Step	Hyp	Ref	Expression
1		syldd.1	. 2 |- (ph -> (ps -> (ch -> th)))
2		syldd.2	. . 3 |- (ph -> (ps -> (th -> ta )))
3		syl1 16	. . 3 |- ((th -> ta ) -> ((ch -> th) -> (ch -> ta )))
4	2, 3	syl6 23	. 2 |- (ph -> (ps -> ((ch -> th) -> (ch -> ta ))))
5	1, 4	mpdd 47	1 |- (ph -> (ps -> (ch -> ta )))

Syntax hints:   -> wi 2

This theorem is referenced by:  prlem934 3933

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

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