Theorem 3syld 51

Description: Triple syllogism deduction. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypotheses

Ref	Expression
3syld.1	|- (ph -> (ps -> ch))
3syld.2	|- (ph -> (ch -> th))
3syld.3	|- (ph -> (th -> ta))

Assertion

Ref	Expression
3syld	|- (ph -> (ps -> ta))

Proof of Theorem 3syld

Step	Hyp	Ref	Expression
1		3syld.1	. . 3 |- (ph -> (ps -> ch))
2		3syld.2	. . 3 |- (ph -> (ch -> th))
3	1, 2	syld 40	. 2 |- (ph -> (ps -> th))
4		3syld.3	. 2 |- (ph -> (th -> ta))
5	3, 4	syld 40	1 |- (ph -> (ps -> 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:  nchoicelem17  6306